Geometry Worksheets

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Semicircle

By Shrinivasa M

Learn about the Semicircle and its use in geometry to solve problems. Find the definition, example problems, and practice problems at Thinkster Math.

Why is this concept useful?

The semicircle is useful in geometry, where we need to determine the area and perimeter, when we come across similar shapes. Real-world situations like an arch, garden, lobby, cake, artwork or woodwork in the form of a semicircular shape, are all of importance to find parameters such as area and perimeter. It is widely used in topics related to area, where we come across different designs and shapes involving semicircles.

Where does this concept fit into the curriculum?

Elementary through High School

What is a Semicircle?

A semicircle is a geometric shape obtained when a circle is cut into two equal halves

along its diameter. It is called a half circle. Any diameter of a circle cuts the circle into two semicircles.The angle formed by the semi circle is 180 degrees.

Boundary of a semicircle includes one half of the circle boundary and the diameter.

How to use the Semicircle:

Semicircle is used to relate to similar shaped objects and determine the area or perimeter. If r represents the radius and d represents the diameter, then we can write:

Area of a semicircle is half the area of a circle = π

r2r^2
/2

Perimeter or circumference is given by πd/2 + d  or  (π  + 2) r

Sample Math Problems

Question

What is the perimeter of a semicircle of radius 10 units?

Answer

Perimeter = π r + 2 r

π(10) + 2(10) = 20 + 10π units

Question

Find the area of a semicircle if the circumference of the circle is 30π units.

Answer

Circumference of circle = 2πr = 30π. So, r = 15 units

Area of semicircle = π

r2r^2
/2 = π
(15)2(15)^2
/2 = 112.5π sq. units

Question

Find the circumference of a semicircle whose area is 24.5π sq units. Take π = 22/7

Answer

Area of semicircle = 24.5π = π

r2r^2
/2, So,
r2r^2
= 49, r = 7 units

Circumference = (π + 2)r = (22/7+2) 7 = 36 units

Question

Find the area of the shaded region in the design.

Answer

Since the side of the square is 14, the radius of the semicircle is 7 units

Shaded region area = Area of square - Area of 2 semi circles

= Area of square - Area of one circle

= 14 x 14 - π

(7)2(7)^2

= 196 - 22/7 (49) = 42 sq units.

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Practice Math Problems

1. Area and arc length of a semicircle are equal. Find the radius.

2. Find the area and perimeter of a semicircle of radius 14 cm. Use π = 22/7

3. Find the area of the shaded region in the following figure if side of square is 10 cm

(Use π = 3.14)

4. Area of a circle is 78.5 square units. Find the perimeter of the semicircle if this circle is cut into half. (Use π = 3.14)

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