Question

to show that the area of a circle is half of product of its circumference and radius i,e area of circle = 1/2×π×r=πr2​

Answer 1

Given:

Circumference of circle = 2πr

Radius of circle = r

To prove:

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

PROOF:

1) The Circumference is the outline of the circle means the length of the boundary of the circle.

2) Radius is the distance from the center of the circle to the boundary of it.

3) As it is given in the question that we have to use the expression of the circumference and radius of the circle.

4) Area of the circle = half of product of the circumference of circle and radius.

LHS

• Area of the circle = πr²

RHS

Half of product of the circumference of circle and radius

• 1/2×2πr × r

• πr²

LHS = RHS

Hence proved.