# Area of a Circle and Semicircle – Formula and Examples

Here you will learn what is the formula for the area of circle and semicircle with examples.

Let’s begin –

## Area of a Circle Formula

Area = $$\pi r^2$$

where r is the radius of the circle.

## Area of Semicircle Formula

Area of Semicircle = $${1\over 2} \pi r^2$$

where r is the radius of the circle.

Example : Find the area of semicircle whose radius is 7 cm.

Solution : Here, radius = 7 cm

Area of the semicircle = $${1\over 2} \pi r^2$$

= $${1\over 2} \times {22\over 7} \times 7^2$$ = 77 $$cm^2$$

Example : Find the area of a circular park whose circumference is 22 m.

Solution : Let the radius of the circle = r meter

The circumference of the circle = 22 m (given)

We know that formula for the circumference is $$2\pi r$$.

$$\implies$$   $$2\pi r$$ = 22

$$\implies$$   r = $$22\over 2\pi$$ = $$22 \times 7\over 2 \times 22$$ = $$7\over 2$$ m

Hence, Area = $$\pi r^2$$ = $$22\over 7$$ $$\times$$ $$7\over 2$$ $$\times$$ $$7\over 2$$ = 38.5 $$m^2$$

Example : If the area and perimeter of the circle are numerically equal, then find the radius of the circle.

Solution : Let the radius of the circle = r

Then, Perimeter of the circle = $$2\pi r$$

And the area of the circle = $$\pi r^2$$

According to the question,

Area of the circle = Perimeter of the circle

$$\implies$$  $$\pi r^2$$ = $$2\pi r$$

Hence, the radius of the circle is 2 units.