Winpossible New York, New York, US,

November 10, 2008

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of ‘Area of Polygons and Circles’. The mini-lessons here include: Getting started, Area of a Rectangle, Area of a Square, Area of a Triangle, Area of a Parallelogram, Area of a Trapezoid, Area of a Circle, Effect of dimension changes on Area, Real World Applications.

- Mathematics > General
- Mathematics > Geometry

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of ‘Area of Polygons and Circles’. The mini-lessons here include: Getting started, Area of a Rectangle, Area of a Square, Area of a Triangle, Area of a Parallelogram, Area of a Trapezoid, Area of a Circle, Effect of dimension changes on Area, Real World Applications.

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here -
Getting Started - Area of Polygons and Circles.

This mini-lesson content introduces and walks you through the basic concepts of area of polygons. You'll learn it with the help of some examples, practice questions and quizzes with solution, using video explanations by the instructor that brings in an element of real-class room experience. The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit i.e. square meters, square inches, or square kilometers etc. To find the area of a square, we count the squares inside the closed figure. But to make it simpler, you can use area formulas instead. Every polygon has a formula for finding its area. For example, if we are given the base of the triangle (b) and the perpendicular height (h); to calculate area use the formula:

1/2 x base(b) x height(h)

This mini-lesson content introduces and walks you through the basic concepts of area of polygons. You'll learn it with the help of some examples, practice questions and quizzes with solution, using video explanations by the instructor that brings in an element of real-class room experience. The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit i.e. square meters, square inches, or square kilometers etc. To find the area of a square, we count the squares inside the closed figure. But to make it simpler, you can use area formulas instead. Every polygon has a formula for finding its area. For example, if we are given the base of the triangle (b) and the perpendicular height (h); to calculate area use the formula:

1/2 x base(b) x height(h)

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Area of a Rectangle.

In this mini- lesson, you'll learn the formula used for calculating area of a rectangle. It will be shared with the help of some examples and practice questions with solution, and using video explanations by the instructor.

A rectangle is a four sided polygon, where opposite sides are parallel and congruent. The area of a rectangle can be obtained by multiplying the lengths of the two sides. If length of one side is*l* and the length of the other side is *w*, then the area of the rectangle is given by the formula:

Area =*l* × *w*.

For example, the area of a rectangular room of dimensions 10 m and 20 m is 200 m^{2}.

The formula for finding the area of a rectangle can also be used to find the length of one side, if we know the area and the dimension of the other side.

length = Area / width.

width = Area/length.

For example: if the area of the rectangle is 120 cm^{2} and the length is 12 cm, then width works out to 120/12 = 10 cm.

In this mini- lesson, you'll learn the formula used for calculating area of a rectangle. It will be shared with the help of some examples and practice questions with solution, and using video explanations by the instructor.

A rectangle is a four sided polygon, where opposite sides are parallel and congruent. The area of a rectangle can be obtained by multiplying the lengths of the two sides. If length of one side is

Area =

For example, the area of a rectangular room of dimensions 10 m and 20 m is 200 m

The formula for finding the area of a rectangle can also be used to find the length of one side, if we know the area and the dimension of the other side.

length = Area / width.

width = Area/length.

For example: if the area of the rectangle is 120 cm

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Area of a Square.

In this mini- lesson,you'll learn the formula used for calculating area of a square. It will be shared with the with the help of some examples and practice questions with solution, using multimedia explanations by the instructor.

The area of a square can be obtained by multiplying the lengths of the two sides. Since the lengths of the sides are the same in a square, you square the length of the side to get the area. In other words the area of a square can be determined by multiplying the base times itself.

If the side of the square is ‘*s*’, then Area = *s* × *s* = *s*^{2}. For example, the area of a square field with side 50 m is 2500 m^{2}. If the area of a square is known, then its side can be calculated by: side of square = ?Area of square.

For example, if the area of a square field is 625 m^{2}, then its side is ?625 = 25 m.

In this mini- lesson,you'll learn the formula used for calculating area of a square. It will be shared with the with the help of some examples and practice questions with solution, using multimedia explanations by the instructor.

The area of a square can be obtained by multiplying the lengths of the two sides. Since the lengths of the sides are the same in a square, you square the length of the side to get the area. In other words the area of a square can be determined by multiplying the base times itself.

If the side of the square is ‘

For example, if the area of a square field is 625 m

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here -
Area of a Triangle.

In this mini- lesson, you'll learn the formulas used for calculating area of triangles. It will be shared with the help of some examples and practice questions with solution, using video explanations by the instructor.

Then you'll practice with some important formulas to calculate the area of triangles. If the base of a triangle is b and the height is h, then the area of the triangle is: ½ × base × height. E.g. if base of a triangle is 20 cm and height 10 cm, then calculated area using above formula is ½ × 20 × 10 = 100 cm^{2}.

If base of the triangle and its area is known, then height is given by: height = 2 × Area/Base. E.g. if the area of a triangle is 300 cm^{2} and height is 10 cm, then base is 60 cm.

If three sides of a triangle a, b, c are given, we can use Heron’s formula:

Area =?((s)(s - a)(s - b)(s - c) where s= (a+b+c)/2

Given the lengths of two sides of a triangle a, b and the measure of angle*C* between them, the following formula can be used: Area of triangle = 1/2 ab sin *C*.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini- lesson, you'll learn the formulas used for calculating area of triangles. It will be shared with the help of some examples and practice questions with solution, using video explanations by the instructor.

Then you'll practice with some important formulas to calculate the area of triangles. If the base of a triangle is b and the height is h, then the area of the triangle is: ½ × base × height. E.g. if base of a triangle is 20 cm and height 10 cm, then calculated area using above formula is ½ × 20 × 10 = 100 cm

If base of the triangle and its area is known, then height is given by: height = 2 × Area/Base. E.g. if the area of a triangle is 300 cm

If three sides of a triangle a, b, c are given, we can use Heron’s formula:

Area =?((s)(s - a)(s - b)(s - c) where s= (a+b+c)/2

Given the lengths of two sides of a triangle a, b and the measure of angle

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Area of a Rhombus.

In this mini-lesson, you'll learn the formula used for calculating area of a rhombus. It will be shared with the help of some examples and practice questions with solution, using multimedia explanations by the instructor.

Here we explain how to calculate the area of a rhombus. To get the area of a rhombus, you need first to draw a line segment (b) from one vertex to another vertex. Following this, draw a perpendicular line segment (h) from a third vertex to the base. The rhombus has now two created triangles, with base (b) and height (h). The area of rhombus will be sum of the area of these two triangles i.e. 2 x ½ x bh = bh.

If the diagonal lengths of a rhombus are*d*_{1} and *d* _{2}, then its area can be calculated by the formula: Area = ½ × *d*_{1} × *d*_{1}. For example, if diagonals of the rhombus are 10 cm and 15 cm, the area works out to: ½ × 10 × 15 = 75 cm^{2}.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini-lesson, you'll learn the formula used for calculating area of a rhombus. It will be shared with the help of some examples and practice questions with solution, using multimedia explanations by the instructor.

Here we explain how to calculate the area of a rhombus. To get the area of a rhombus, you need first to draw a line segment (b) from one vertex to another vertex. Following this, draw a perpendicular line segment (h) from a third vertex to the base. The rhombus has now two created triangles, with base (b) and height (h). The area of rhombus will be sum of the area of these two triangles i.e. 2 x ½ x bh = bh.

If the diagonal lengths of a rhombus are

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Area of a Parallelogram.

In this mini- lesson, you'll learn the formulas used for calculating area of a parallelogram. It will be shared with the help of some examples and practice questions with solution, and watching video as well as explanations by the instructor.

The area, A, of a parallelogram is A = BH, where B is the base of the parallelogram and H is its height. The height of a parallelogram is a segment drawn perpendicular to the base from an opposite vertex. In another way the area of a parallelogram is twice the area of a triangle created by one of its diagonals.

For example, if base of a parallelogram is 20 cm and height is 10 cm, then area is given by 20 × 10 = 200 cm^{2}.

If base of a parallelogram and its area is known, then height is given by:

height = Area/Base.

E.g. if the area of a parallelogram is 100 cm^{2} and base is 5 cm, then height is 100/5 = 20 cm.

Similarly, when height of a parallelogram and its area are known, then base can be calculated by:

base= Area/height,

E.g. if the area of a parallelogram is 50 cm^{2} and height is 10 cm, then base is 50/10 = 5 cm.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini- lesson, you'll learn the formulas used for calculating area of a parallelogram. It will be shared with the help of some examples and practice questions with solution, and watching video as well as explanations by the instructor.

The area, A, of a parallelogram is A = BH, where B is the base of the parallelogram and H is its height. The height of a parallelogram is a segment drawn perpendicular to the base from an opposite vertex. In another way the area of a parallelogram is twice the area of a triangle created by one of its diagonals.

For example, if base of a parallelogram is 20 cm and height is 10 cm, then area is given by 20 × 10 = 200 cm

If base of a parallelogram and its area is known, then height is given by:

height = Area/Base.

E.g. if the area of a parallelogram is 100 cm

Similarly, when height of a parallelogram and its area are known, then base can be calculated by:

base= Area/height,

E.g. if the area of a parallelogram is 50 cm

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Area of a Trapezoid.

In this mini- lesson, you'll learn the formula used for calculating area of a trapezoid. It will be shared with the help of some examples and practice questions with solution, and watching video as well as explanations by the instructor.

You know from earlier learnings that a trapezoid is a 4-sided figure with one pair of parallel sides. To find the area of a trapezoid; take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2. Here the height is the length of segment drawn perpendicular to the base from an opposite vertex. If h is the height and b_{1} and b_{2} are bases of a trapezoid, then its area is: ½ × height × (Sum of bases) i.e. = ½ × h × (b_{1} + b_{1}). For example, if height of a trapezoid is 8 inches and bases of trapezoid measure 13 and 15 inches, the area is given by = ½ × 8 × (13 + 15) which works out to 112 inches^{}.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini- lesson, you'll learn the formula used for calculating area of a trapezoid. It will be shared with the help of some examples and practice questions with solution, and watching video as well as explanations by the instructor.

You know from earlier learnings that a trapezoid is a 4-sided figure with one pair of parallel sides. To find the area of a trapezoid; take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2. Here the height is the length of segment drawn perpendicular to the base from an opposite vertex. If h is the height and b

Member Rating

Curriki Rating**'P'** - This is a trusted Partner resource P**'P'** - This is a trusted Partner resource

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Area of a Circle.

In this mini-lesson, you'll learn the formulas used for calculating area of circles. It will be shared with the help of some examples and practice questions with solution, and watching video as well as explanations by the instructor in own handwriting.

You know from earlier learnings that a circle is a set of points in a plane at the same distance from a point called the center. The radius of a circle is the distance from the center to any point on the circle. The diameter,*d* of a circle is equal to twice the radius i.e. *d* = 2*r*. If point *A* and point *B* are on the circle with center *C*, *AB* = *AC* = *r* = Radius of the circle. To find the area of a circle you can use formula: Area = *r*^{2}. For example, when a radius of a circle is 4 cm, its area is x 4^{2} i.e. 50.24 cm^{2}.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini-lesson, you'll learn the formulas used for calculating area of circles. It will be shared with the help of some examples and practice questions with solution, and watching video as well as explanations by the instructor in own handwriting.

You know from earlier learnings that a circle is a set of points in a plane at the same distance from a point called the center. The radius of a circle is the distance from the center to any point on the circle. The diameter,

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Effect of dimension changes on Area.

In this mini-lesson you’ll learn, with the help of several examples and solution, to determine how a change in dimensions in the figure affects the area. It will be explained by instructor using video and in own handwriting.

You know from earlier learnings that the area of a circle changes with the square of its diameter. E.g. doubling the diameter quadruples the area and tripling the diameter makes the area go up by a factor of nine. Now let us compare a case of 12- inch pizza and 14-inch pizza i.e. increase in diameter by 2 inches: the percentage change in radius is 16.7% and percentage change in area is 36.1%. More examples of area of polygons - when the length of a rectangle is tripled and its width stays the same, its area will be three times the original area. Similarly, if one of the diagonals of a rhombus is doubled, its area is doubled. In case of a trapezoid, if the length of parallel sides and the distance between them are all doubled, then the new area becomes 4 times of the original area.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini-lesson you’ll learn, with the help of several examples and solution, to determine how a change in dimensions in the figure affects the area. It will be explained by instructor using video and in own handwriting.

You know from earlier learnings that the area of a circle changes with the square of its diameter. E.g. doubling the diameter quadruples the area and tripling the diameter makes the area go up by a factor of nine. Now let us compare a case of 12- inch pizza and 14-inch pizza i.e. increase in diameter by 2 inches: the percentage change in radius is 16.7% and percentage change in area is 36.1%. More examples of area of polygons - when the length of a rectangle is tripled and its width stays the same, its area will be three times the original area. Similarly, if one of the diagonals of a rhombus is doubled, its area is doubled. In case of a trapezoid, if the length of parallel sides and the distance between them are all doubled, then the new area becomes 4 times of the original area.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Real World Applications.

In this mini-lesson you’ll learn, with the help of several examples and solution, how to solve the problems involving real-world applications. Real world problems may include areas and perimeters of rectangles and triangles, volumes of boxes, other polygons etc. The over view of earlier learning including using the formulae for area of polygons will help you to apply the concepts and relationships in geometry to find solution to the application related problems. Let us look at an example: area of a walkway path in the garden, of outside length 25 m and width 20 m, the width of walkway path being 2 m, is 164 m^{2}. To determine area of the path, follow the steps:

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini-lesson you’ll learn, with the help of several examples and solution, how to solve the problems involving real-world applications. Real world problems may include areas and perimeters of rectangles and triangles, volumes of boxes, other polygons etc. The over view of earlier learning including using the formulae for area of polygons will help you to apply the concepts and relationships in geometry to find solution to the application related problems. Let us look at an example: area of a walkway path in the garden, of outside length 25 m and width 20 m, the width of walkway path being 2 m, is 164 m

- Find the area of large rectangle = 25 x 20=500 m
^{2} - Find the area of small rectangle = (25 - 2 - 2) x (20 - 2 - 2) = 336 m
^{2} - Area of path = Area of large rectangle – Area of small rectangle = 164 m
^{2}

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