Perimeter of a Semicircle and a Quarter Circle

Learn to find the total distance around partial circles

1. Perimeter of a Semicircle

What is a Semicircle?

A semicircle is half of a circle. Its perimeter consists of:

The curved part (arc) = half the circumference
The straight part = diameter

The Semicircle

Perimeter of semicircle = Arc length + Diameter

= $\frac{1}{2} \times \pi \times d + d$

or = $\pi r + 2r$ (when radius is given)

Example 1: Diameter Given $(\text{Take } \pi = 3.14)$

The diameter of a semicircle is 10 cm. Find its perimeter.

Solution:

Circumference = $\pi$ × Diameter = 3.14 × 10 = 31.4 cm

Arc length = 31.4 ÷ 2 = 15.7 cm

Perimeter of semicircle = 15.7 + 10 = 25.7 cm

Example 2: Radius Given $(\text{Take } \pi = \frac{22}{7})$

Find the perimeter of the semicircle. The radius is 28 cm.

Solution:

Arc length = $\frac{1}{2} \times 2 \times \pi \times r = \frac{1}{2} \times 2 \times \frac{22}{7} \times 28$ = 88 cm

Perimeter = Arc length + Radius + Radius

= 88 + 28 + 28 = 144 cm

2. Perimeter of a Quarter Circle

What is a Quarter Circle?

A quarter circle is one quarter of a circle. Its perimeter consists of:

The curved part (arc) = one quarter of the circumference
Two straight edges = radius + radius

The Quarter Circle

Perimeter of quarter circle = Arc length + Radius + Radius

= $\frac{1}{4} \times 2\pi r + r + r$

Example: $(\text{Take } \pi = 3.14)$

Find the perimeter of the quarter circle with radius 5 cm.

Solution:

Circumference = 2 × $\pi$ × r = 2 × 3.14 × 5 = 31.4 cm

Arc length = 31.4 ÷ 4 = 7.85 cm

Perimeter = 7.85 + 5 + 5 = 17.85 cm

3. Perimeter of a Three-Quarter Circle

Three-Quarter Circle

A three-quarter circle is three quarters of a circle. Its perimeter consists of:

The curved part (arc) = three quarters of the circumference
Two straight edges = radius + radius

Example: $(\text{Take } \pi = \frac{22}{7})$

Find the perimeter of the figure. The radius is 14 cm.

Solution:

Arc length = $\frac{3}{4} \times 2 \times \pi \times r$

= $\frac{3}{4} \times 2 \times \frac{22}{7} \times 14$ = 66 cm

Perimeter = 66 + 14 + 14 = 94 cm

4. Practice Problems

Problem 1 $(\text{Take } \pi = \frac{22}{7})$

Find the perimeter of the semicircle. Diameter = 35 cm.

ShowHide solution

Arc length = $\frac{1}{2} \times \frac{22}{7} \times 35$ = 55 cm

Perimeter = 55 + 35 = 90 cm

Problem 2 $(\text{Take } \pi = 3.14)$

Find the perimeter of the quarter circle. Radius = 8 m. Round your answer to the nearest whole number.

ShowHide solution

Circumference = 2 × 3.14 × 8 = 50.24 m

Arc length = 50.24 ÷ 4 = 12.56 m

Perimeter = 12.56 + 8 + 8 = 28.56 m ≈ 29 m

Problem 3 $(\text{Take } \pi = 3.14)$

Find the perimeter of the semicircle. Radius = 20 m.

ShowHide solution

Arc length = $\pi \times r$ = 3.14 × 20 = 62.8 m

Diameter = 2 × 20 = 40 m

Perimeter = 62.8 + 40 = 102.8 m

Problem 4 $(\text{Take } \pi = 3.14)$

Find the perimeter of the quarter circle. Radius = 4.5 cm. Give your answer correct to 2 decimal places.

ShowHide solution

Circumference = 2 × 3.14 × 4.5 = 28.26 cm

Arc length = 28.26 ÷ 4 = 7.065 cm

Perimeter = 7.065 + 4.5 + 4.5 = 16.065 cm ≈ 16.07 cm

Key Takeaways

Semicircle perimeter = Arc ( $\frac{1}{2}$ circumference) + Diameter

Quarter circle perimeter = Arc ( $\frac{1}{4}$ circumference) + Radius + Radius

Three-quarter circle perimeter = Arc ( $\frac{3}{4}$ circumference) + Radius + Radius

Always identify the curved parts and straight parts before calculating!

Perimeter of a Semicircle and a Quarter Circle

1. Perimeter of a Semicircle

What is a Semicircle?

The Semicircle

Example 1: Diameter Given (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

Example 2: Radius Given (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

2. Perimeter of a Quarter Circle

What is a Quarter Circle?

The Quarter Circle

Example: (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

3. Perimeter of a Three-Quarter Circle

Three-Quarter Circle

Example: (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

4. Practice Problems

Problem 1 (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

Problem 2 (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

Problem 3 (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

Problem 4 (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

Key Takeaways

Example 1: Diameter Given $(\text{Take } \pi = 3.14)$

Example 2: Radius Given $(\text{Take } \pi = \frac{22}{7})$

Example: $(\text{Take } \pi = 3.14)$

Example: $(\text{Take } \pi = \frac{22}{7})$

Problem 1 $(\text{Take } \pi = \frac{22}{7})$

Problem 2 $(\text{Take } \pi = 3.14)$

Problem 3 $(\text{Take } \pi = 3.14)$

Problem 4 $(\text{Take } \pi = 3.14)$