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.

Also Read : Formula for Circumference of Circle (Perimeter) – Examples

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.

Leave a Comment

Your email address will not be published.