Question

The formula for the area of a circle can be found by using a parallelogram. Explain the way to derive the formula.

Answer 1

Answer:

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The circle can be cut into slices, separated, and fit together to form a parallelogram that has the same area. The height of the parallelogram is the radius and the base is half the circumference, which is r. The area is r(r), which is equal to r2.

Step-by-step explanation:

Answer 2

The area of circle is product of the circumference of the circle and its radius. The formula to find the area of the circle is derived using parallelogram is,

$A= \pi \times r^2$

What is the area of the circle?

The area of circle is product of the circumference of the circle and its radius.

Ways to derive the formula of a are of a circle using a parallelogram are,

• Step 1- With the help of a compass draw a circle on a paper and cut it out.

• Step 2- Fold this paper three times with equal side as shown in attached images. Unfold the circle and cut all the parts are shown by folded lines.

• Step 3-Arrange all these equal parts of the circle in a parallelogram form.

Here we can see that the base $b$ of the parallelogram is equal to the perimeter of the circle with radius r. Therefore ,

$b=\pi r$

Now look at the height $h$ of the parallelogram. This is equal to the radius of the circle. Therefore,

$h=r$

The formula for the area of the parallelogram can be given as,

$A=b\times h$

Put the value,

$A=\pi \times r\times r$

$A= \pi \times r^2$

Hence, the formula to find the area of the circle is derived using parallelogram is,

$A= \pi \times r^2$

For more about the area of the circle follow the link below-

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