Area of Semicircle – Formula, Steps, Examples & How to Find It

Area of Semicircle

Area of a semicircle is the space inside half of a circle. Since a semicircle is exactly one-half of a full circle, its area is also half of the circle’s area. In simple words, if you cut a round shape like a pizza into two equal parts, the area of one part is the area of the semicircle. The area of semicircle formula is (1/2) × πr², where r is the radius. In this topic, we will understand what is the area of a semicircle is, and learn how to find the area of a semicircle with solved examples.

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What is Area of a Semicircle?

Area of a semicircle is the measure of space enclosed within half of a circle. A semicircle is formed when a circle is divided into two equal parts along its diameter. Since it represents one-half of a full circle, its area is also exactly half of the circle’s area. In everyday life, you can see semicircle shapes in arches, windows, and playground designs. Learning the area of a semicircle helps students easily solve geometry problems and understand real-world applications.

For example:

• If you cut a round pizza into two halves, the space inside one half is the area of a semicircle.

• If a round playground is divided into two halves, each part has an area equal to half of the circle.

Read More: What is a Polyhedron

Area of a Semicircle Formula

The area of a semicircle formula helps us calculate the space inside half of a circle. Since a semicircle is exactly one-half of a circle, its area is also half of the circle’s area. This formula is very useful for solving geometry questions and also in daily life situations like finding the space of half-round gardens, windows, or pizza slices.

Semicircle Arrea Formula Explanation: 

We know that the area of a circle is πr².
Where,

• r = radius (distance from the centre to the edge)

• π (pi) ≈ 3.14
  So, to find the area of a semicircle, just divide the circle’s area by 2.

How to Find Area of a Semicircle

Finding the area of a semicircle becomes easy if you follow a step-by-step method. The formula alone may look tricky, but breaking it into small steps helps students understand it better. Whether you are solving a school problem or calculating space in real life, these steps will guide you on how to find the area of a semicircle correctly. By practicing, students can quickly apply the area of semicircle formula and avoid mistakes while solving geometry questions. Below are the steps on how to find the area of a semicircle:

• Measure the radius of the semicircle.

• Square the radius (multiply it by itself).

• Multiply by π (3.14).

• Divide the result by 2.

Read More: Counting Numbers

Area of a Semicircle Examples

Examples help us understand the area of the semicircle formula in real problems. By solving step-by-step, students learn how to find the area of a semicircle using radius or diameter. These examples make the concept simple and clear. Below are some examples of area of semicircle:

Area of a Semicircle Example 1

Question: Find the area of a semicircle with radius 4 cm.
Solution: Area = (1/2) × πr²
= (1/2) × 3.14 × 4²
= (1/2) × 3.14 × 16
= 25.12 cm²

Area of a Semicircle Example 2

Question: The diameter of a semicircle is 10 cm. Find its area.
Solution: Radius = Diameter ÷ 2 = 10 ÷ 2 = 5 cm
Area = (1/2) × 3.14 × 5²
= (1/2) × 3.14 × 25
= 39.25 cm²

Area of a Semicircle Example 3

Question: A semicircle has a radius of 7 m. Calculate its area.
Solution: Area = (1/2) × 3.14 × 7²
= (1/2) × 3.14 × 49
= 76.93 m²

Area of a Semicircle Example 4

Question: Find the area of a semicircle when radius = 14 cm.
Solution: Area = (1/2) × 3.14 × 14²
= (1/2) × 3.14 × 196
= 307.72 cm²

Area of a Semicircle Example 5

Question: The radius of a semicircle is 21 cm. What is the area?
Solution: Area = (1/2) × πr²
= (1/2) × 3.14 × (21 × 21)
= (1/2) × 3.14 × 441
= 691.47 cm²
Answer: 691.47 cm²

Area of a Semicircle Example 6

Question: A semicircular window has a radius of 3 m. Find its area.
Solution: Area = (1/2) × πr²
= (1/2) × 3.14 × (3 × 3)
= (1/2) × 3.14 × 9
= 14.13 m²
Answer: The area of the window is 14.13 m².

Area of a Semicircle Example 7

Question: A pizza is cut into two equal halves. If the radius of the pizza is 7 cm, what is the area of one-half?
Solution: Area = (1/2) × πr²
= (1/2) × 3.14 × (7 × 7)
= (1/2) × 3.14 × 49
= 76.93 cm²
Answer: Each half-pizza has an area of 76.93 cm².

Area of a Semicircle Example 8

Question: A playground is in the shape of a semicircle with a diameter of 20 m. Find the area of the playground.
Solution: Radius = Diameter ÷ 2 = 20 ÷ 2 = 10 m
Area = (1/2) × πr²
= (1/2) × 3.14 × (10 × 10)
= (1/2) × 3.14 × 100
= 157 m²
Answer: The semicircular playground has an area of 157 m².

Area of a Semicircle Example 9

Question: A semicircular garden has a radius of 14 m. Find its area.
Solution: Area = (1/2) × πr²
= (1/2) × 3.14 × (14 × 14)
= (1/2) × 3.14 × 196
= 307.72 m²
Answer: The garden covers an area of 307.72 m².

Area of a Semicircle Example 10

Question: A school gate has a semicircular arch of radius 5 m. What is the area of the arch?
Solution: Area = (1/2) × πr²
= (1/2) × 3.14 × (5 × 5)
= (1/2) × 3.14 × 25
= 39.25 m²
Answer: The area of the arch is 39.25 m².

Read More: Euler's Formula

Perimeter of a Semicircle

Apart from the area, students also learn about the perimeter of a semicircle. The perimeter means the total length around the semicircle. It includes both the curved edge (half of the circle) and the straight edge (the diameter). Knowing the perimeter is useful in real-life cases like fencing a semicircular park or designing gates and windows.

Formula:
Perimeter = πr + 2r

Here, πr is the curved part and 2r is the straight line (diameter).

Perimeter of a Semicircle Practice Questions

Learning becomes stronger when we solve questions on our own. Here are some mixed practice problems to check your understanding of the area of a semicircle formula and its applications.

Perimeter of a Semicircle Question 1

Find the area of a semicircle with radius 6 cm.
a) 56.52 cm²
b) 62.83 cm²
c) 113.04 cm²
d) 38 cm²

Answer: a) 56.52 cm²

Perimeter of a Semicircle Question 2

The diameter of a semicircle is 12 cm. What is its area?
a) 113.04 cm²
b) 56.52 cm²
c) 72 cm²
d) 90.25 cm²

Answer: b) 56.52 cm²

Perimeter of a Semicircle Question 3

A park is shaped like a semicircle with a radius of 10 m. Find its area.
a) 314 m²
b) 157 m²
c) 200 m²
d) 250 m²

Answer: b) 157 m²

Perimeter of a Semicircle Question 4

What does the area of a semicircle mean?
a) The length around half a circle
b) The space inside half of a circle
c) The distance across a circle
d) The curved boundary of a circle

Answer: b) The space inside half of a circle

Perimeter of a Semicircle Question 5

Why do we divide the circle’s area by 2 to find the semicircle’s area?
a) Because it is smaller than a square
b) Because a semicircle is half of a circle
c) Because the radius is divided by 2
d) Because the diameter is smaller

Answer: b) Because a semicircle is half of a circle

Perimeter of a Semicircle Question 6

Find the area of a semicircle with radius 7 cm.
a) 38.5 cm²
b) 76.93 cm²
c) 49 cm²
d) 100 cm²

Answer: b) 76.93 cm²

Perimeter of a Semicircle Question 7

The diameter of a semicircle is 14 cm. What is its area?
a) 76.93 cm²
b) 100 cm²
c) 154 cm²
d) 49 cm²

Answer: a) 76.93 cm²

Perimeter of a Semicircle Question 8

Which formula is correct for the area of a semicircle?
a) πr²
b) (1/2) × πr²
c) 2πr
d) πr + 2r

Answer: b) (1/2) × πr²

Perimeter of a Semicircle Question 9

What is the perimeter of a semicircle formula?
a) 2πr
b) πr²
c) πr + 2r
d) (1/2) × πr²

Answer: c) πr + 2r

Perimeter of a Semicircle Question 10

A semicircular arch has a radius of 5 m. What is its area?
a) 25 m²
b) 39.25 m²
c) 78.5 m²
d) 50 m²

Answer: b) 39.25 m²

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