Question

To explain how the formula for area, A=bh

, can be used to derive the formula for the area of a circle, start by taking a circle, dividing it into small pizza shaped slices, and laying the slices out as shown.



The smaller the slices are, the less curvature and the closer to a parallelogram the shape becomes.

The base of the parallelogram, in terms of the circle, is
, and the height of the parallelogram is
.

Area is base times height, so multiply the base and the height together.

Now we have the formula area =
.

Answer 1

bh, where b is the base and h is the height of the parallelogram.

In the case of the circle, the base of the parallelogram is the circumference of the circle, which is equal to 2πr, where r is the radius of the circle. The height of the parallelogram is the distance from the center of the circle to the edge of the circle, which is also the radius r. Therefore, we have:

b = 2πr

h = r

Substituting these values into the formula for the area of a parallelogram, we get:

Area = bh = (2πr)(r) = 2πr^2

So the formula for the area of a circle is derived from the formula for the area of a parallelogram by using the circumference of the circle as the base and the radius of the circle as the height.