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

The way to derive the formula for the area of a circle can be found by using a parallelogram is as follows: 1.  using  a compass, draw a circle and cut it out.2. carefully fold the circle three times to get 8 equal wedges.3.  unfold the circle and shade one-half of the circle (this means 4 wedges will be shaded while the other  4 will be unshaded)4.  cut out the wedges5.  place the wedges side-by-side in this order -shaded | unshaded |  shaded | unshaded | shaded | unshaded | shaded | unshaded(the shaded wedges should face up while the unshaded wedges should face down. this forms a figure that looks like a parallelogram)ps. check the attached picture to see how the base and height of the parallelogram relate to the parts of the circle.

the base of the parallelogram, b = half of the circumference of the circle.

half of the circumference of the circle =  πr

therefore, b =  πr

the height of parallelogram, h  =  the radius of the circle

therefore, h = r

area of  a parallelogram = bh

to find the area of the circle, let's substitute  πr  for b and r for h  in the above formula.

area of the circle =  πr * r

area of the circle =  πr²hence, the formula to find area of a circle is  πr²