# FINDING THE AREA OF A CIRCLE USING A PARALLELOGRAM

## About "Finding the area of a circle using a parallelogram"

Finding the area of a circle using a parallelogram :

In this section, we are going to see, how the formula for area of a circle can be derived using a parallelogram.

## Finding the area of a circle using a parallelogram

Step 1 :

Use a compass to draw a circle and cut it out.

Step 2 :

Fold the circle three times as shown to get equal wedges.

Step 3 :

Unfold and shade one-half of the circle.

Step 4 :

Cut out the wedges, and fit the pieces together to form a figure that looks like a parallelogram.

The base and height of the parallelogram relate to the parts of the circle.

Base b  =  Half of the circumference of the circle.

or b  =  πr

Height h  =  radius of the circle

or h  =  r

We know that the formula to find area of the parallelogram is

A  =  bh

To find the area of the circle, substitute πr for b and r for h in the above area formula.

A  =   πr x r

A  =   πr²

Hence, the formula to find area of a circle is πr² square units.

Reflect :

How can we make the wedges look more like a parallelogram ?

Make the wedges smaller so the base looks more like a straight line than curves.

## Finding area of a circle

Example 1 :

Find the area of a circle whose radius is 7 cm.

Solution :

Step 1 :

Area of a circle  =  πr²

Radius is given in the question. That is 7 cm.

Plug r  =  7  in the above formula.

Area of the circle  =  π(7)²

Step 2 :

Since radius is a multiple of 7, we can use π    22/7.

Area of the circle    (22/7) x (7)²

Simplify

Area of the circle    22 x 7

Area of the circle    154 square cm.

Hence, the area of the circle is about 154 square cm.

Example 2 :

Find the area of a circle whose diameter is 40 inches.

Solution :

Step 1 :

Area of a circle  =  πr²

We know that

Radius  =  Diameter / 2

Radius  =  40/2  =  20 inches

Step 2 :

Plug r  =  20  in the above formula.

Area of the circle  =  π(20)²

Step 3 :

Since radius is not a multiple of 7, we can use π    3.14.

Area of the circle    (3.14) x (20)²

Area of the circle    3.14 x 400

Area of the circle    1256 square in.

Hence, the area of the circle is about 1256 square in.

After having gone through the stuff given above, we hope that the students would have understood "Finding the area of a circle using a parallelogram".

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