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.
