Area of a circle

You have already learnt to find the area of a trapezium and parallelogram. Also, you have learnt to find the area of a triangle, rectangle and square. How can the area of the circle be obtained?

You might have observed that the length of the rectangle you constructed is half the circumference of the circle. Therefore,

Length of the rectangular shape = $\frac{\text{Circumference of the circle}}{2}$

= $\frac{2\pi r}{2}$

= $\pi r$

Also, the width of the rectangular shape is the same as the radius of the circle. Therefore, the area of a circle can be obtained by calculating the area of the rectangle constructed. This is possible because the length and width of the rectangle constructed are known.

Therefore,

The area of a circle = Area of rectangular shape

= length × width

= $\pi r \times r$

= $\pi r^2$

Therefore, the area of a circle is $\pi r^2$ where $r$ is the radius of the circle.

Now, use this formula to calculate the area of the circle. Thereafter, compare the answer with the area of the rectangular shape you have constructed.

Use $\pi = 3.14$. The answers are expected to be approximately the same.

Since, diameter ($d$) = 2 × radius ($r$)

$= 2r$

$d = 2r$

$r = d/2$

Thus, area of a circle = $\frac{\pi d^2}{4}$

Therefore, area of a circle = $\frac{\pi d^2}{4}$

where $r$ is the radius and $d$ is the diameter of the circle.