Semicircle Formulas with Solved Examples

Semicircle Formulas

A semicircle is indeed a plane figure made by splitting a circle into exactly two halves in geometry. So, using the perimeter and area of a circle, we can create the formulas for the perimeter and area of a semicircle.

Definition

When a lining travelling through the centre reaches the circle’s two ends, it forms a semicircle. As a result, we create a circular shape by combining two semicircles. A semi-circular shape is formed when a circle is sliced in half and when the circle is split by two. Because the area of a semicircle is half the same as a circle, the area is also half the same as a circle. The diameter of a circle is shown by the line AC in the diagram below. The diameter splits the circle into two parts, each of which has the same area. The semicircles are the two halves of the circle.

Area of Semicircle Formula

A semicircle has half the surface area of a circle. Because the radius of a circle is πr², so a semicircle’s area is 1/2(πr²), wherein r is the radius and the value of π = 3.14 or 22/7.

Perimeter of Semicircle Formula

A semicircle’s perimeter is equal to half of the circle’s circumference plus its diameter. The circumference of a circle is 2πr or πd. A semicircle’s perimeter is 1/2 (πd) + d or πr + 2r, here r is the radius.

Examples

Example 1: Find out the area of the semicircle whose radius is 10cm

Solution: r = 14cm

Area of semi-circle = (πr²)/2

= ½ * (22/7)*14*14

= 308 cm²

Hence the area of the semicircle is 308cm²

Example 2: Find the perimeter of a semicircle with a radius of 3.5cm

Solution: We have the radius r = 3.5

Perimeter of the semicircle = πr + 2r

Perimeter = 22/7*3.5 + 7

Perimeter = 18 cm (Answer)

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