How to Find the Area and Perimeter of the Semicircle?

A semicircle is a semicircle. It is a two-dimensional shape that is formed when a circle is cut into two equal parts. In this step-by-step guide, you will learn how to find the area and perimeter of the semicircle.

How to Find the Area and Perimeter of the Semicircle?

The circumference of a semicircle is the length of the arc that is half of the circle’s circumference, and the perimeter of a semicircle is the sum of its circumference and diameter.

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A step-by-step guide to finding the area and perimeter of the semicircle

If a circle is cut in half along the diameter, that half-circle is called a semicircle. The two halves are equal in size. A semicircle can also be called a half-disk and represents a circular paper plate folded into halves. There is a line of symmetry in the semicircle which is considered the reflection symmetry. Since a semicircle is half a circle, which is \(360°\), the semicircle arc is always \(180°\).

The image below shows a semicircle \(PQR\) along the arc and the diameter \((PQ)\) with both endpoints. Here, point \(J\) is the center, and \(PJ\) and \(JQ\) are the radii of the semicircle.

Area of a semicircle

The area of a circle refers to the area or interior space of the circle. Since we know that a semicircle is half a circle, the area of a semicircle will be half the area of a circle.

Area of a semicircle \(=\color{blue}{\frac{πR^2}{2}}\)

where,

\(R\) is the radius of the semicircle

Circumference of a semicircle

The circumference of a semicircle is defined as the measurement of the arc that forms a semicircle. It does not include the length of the diameter. The circumference of a semicircle is half of the circle’s circumference.

Circumference of a semicircle \(=\color{blue}{\frac{2πR}{2}= πR}\)

Semicircle perimeter

The perimeter of a semicircle is the sum of its circumference and diameter. To calculate the perimeter of a semicircle, we need to know the diameter or radius of the circle along with the length of the arc. To determine the length of the arc, we need the circumference of a semicircle.

Since the circumference is \(C = πR\), where \(C\) is the circumference, and \(R\) is the radius, we can define the formula for the perimeter of a semicircle which is:

The perimeter of a semicircle \(=\color{blue}{(πR + 2R)}\) units, or after factoring the \(R\), the perimeter of a semicircle \(=\color{blue}{R(π + 2)}\)

where,

  • \(R\) is the radius of the semicircle

Finding the Area and Perimeter of the Semicircle – Example 1:

Find the circumference of a semicircle with a diameter of \(10\) units. \(π=3.14\)

Solution:
The diameter is \(=10\) units. So, radius \(= \frac{10}{2} = 5\) units.
The formula to calculate the circumference of a semicircle is \(πR\). Therefore, by substituting the values of \(π\) and radius in this formula, we get:

Circumference \(=3.14× 5\) units

Circumference \(=15.70\) units

Exercises for Finding the Area and Perimeter of the Semicircle

  1.  Calculate the area of a semicircle whose radius is \(8\) inches. \(π=3.14\)
  2. Find the circumference of a semicircle with a diameter of \(46\) inches. \(π=3.14\)
  3. What is the area of the semicircle if the perimeter of the semicircle is \(156\) units?
This image has an empty alt attribute; its file name is answers.png
  1. \(\color{blue}{100. 48 \space in^2}\)
  2. \(\color{blue}{118. 22 \space in^2}\)
  3. \(\color{blue}{1446}\)

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