Area of Semicircles and Quarter Circles

Show your work for each problem.

1.
What is the formula for the area of a semicircle?
1. a)
2. b)
3. c)
4. d)
Answer:
Since a semicircle is half of a circle, we take the circle area formula and divide by 2: .
2.
What is the formula for the area of a quarter circle?
1. a)
2. b)
3. c)
4. d)
Answer:
A quarter circle is one-fourth of a full circle, so we divide the circle area by 4: .
3.
A semicircle has a radius of 2 cm. What is its area in terms of ? (Enter just the number before )
Answer: 2
square cm. The answer is 2.
4.
A quarter circle has a radius of 4 m. What is its area in terms of ? (Enter just the number before )
Answer: 4
square m. The answer is 4.
5.
If a semicircle has radius 6 cm, what is its area?
1. a) cm²
2. b) cm²
3. c) cm²
4. d) cm²
Answer: cm²
cm².
6.
A semicircle has a diameter of 10 cm. What is its area in terms of ? (Enter the number before )
Answer: 12.5
Radius = 10 ÷ 2 = 5 cm. cm².
7.
Calculate the area of a semicircle with radius 8 m. Give your answer in terms of .
Answer: 32π
1. What is the formula for the area of a semicircle? πr²/2
2. What is when ? 64
3. Calculate : 32π
8.
A quarter-circle shaped mat has a radius of 10 cm. Calculate its area in terms of .
Answer: 25π
1. What is the formula for the area of a quarter circle? πr²/4
2. What is when ? 100
3. Calculate : 25π
9.
A semicircular window has a diameter of 14 cm. What is its area? (Use )
1. a)38.47 cm²
2. b)307.72 cm²
3. c)153.86 cm²
4. d)76.93 cm²
Answer: 76.93 cm²
Radius = 14 ÷ 2 = 7 cm. cm².
10.
Find the radius of a semicircle if its area is cm².
Answer: 6
1. Write the equation using the area formula: . Multiply both sides by 2: 36π
2. Divide both sides by to get 36
3. Take the square root to find 6
11.
Two semicircles together form a full circle. If one semicircle has area cm², what is the area of the full circle in terms of ? (Enter just the number)
Answer: 16
Since a semicircle is half of a circle, the full circle has twice the area: cm².
12.
A garden has a semicircular flower bed with radius 5 m and a quarter-circle pond with radius 4 m. What is the combined area? (Use )
Answer: 51.81
1. Calculate the semicircle area: 39.25
2. Calculate the quarter circle area: 12.56
3. Add both areas together: 51.81
13.
Four quarter circles of radius 3 cm are arranged to form a full circle. What is the total area?
1. a) cm²
2. b) cm²
3. c) cm²
4. d) cm²
Answer: cm²
4 quarter circles = 1 full circle. Area = cm².
14.
A three-quarter circle has a radius of 8 cm. What is its area in terms of ?
Answer: 48π
1. What fraction of a full circle is three-quarters? 3/4
2. Calculate the full circle area: 64π
3. Multiply by 3/4: 48π
15.
A quarter circle has an area of m². What is the radius in meters?
Answer: 8
→ → → m.
16.
A semicircle with radius has the same area as a quarter circle with radius . What is the relationship between and ?
1. a)
2. b)
3. c)
4. d)
Answer:
→ → .