The area of the semi-circle is the measure of the amount of surface bounded by the semi-circle. The area of a semi-circle is half of the area of a circle. When a circle is divided into two equal parts, each part is called the area of a semi-circle. The total area of a semi-circle is 180°. On this page, we will discuss the area of a semicircle in detail.
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How to find the area of a semi-circle.
The area of an enclosed region (semi-circle) is measured to find the size of a standard unit area that can fit in it. Since the area of a semi-circle is half the area of a circle. The formula for finding the area of a semi-circle is 1/2 × πr2, where π = 22/7 and r = radius of the circle.
let’s understand the area of a semi-circle by working through some examples.
How to find the area of semi-circle when the radius of the circle is given.
Example 1. If the radius of a circle is 7cm find the area of the semi-circle. [Take π=22/7]
Solution
The area of a semicircle = 1/2 ×πr2, where π = 22/7 and r = 7cm
= 1/2 × 22/7 × 72
= 1/2 × 22 × 7
= 154/2
= 77cm2
∴ The area of a semi-circle = 77cm2
How to find the area of a semi-circle when the area of a circle is given.
Example 2. If the area of a circle is 48cm2. Find the area of the semi-circle.
Solution
The area of a semi-circle = 1/2 × πr2, since the area of a circle = πr2 = 48cm2
= 1/2 × 48cm2
= 24cm2
∴ The area of a semi-circle = 24cm2