Area of Semicircles and Quarter Circles
Written by Adi Ackerman, Head Teacher
"Area of Semicircles and Quarter Circles" is written for 8th Grade (Ages 13-14). A 7th grader who is already steady on geometry can use it too, and an older student can use it as a short review.
8th grade math worksheet: find the area of 12 semicircles and quarter circles from a radius or diameter, such as d = 12 cm. Answer key included. Part of our semicircles and quarter circles geometry collection.
How do I use this worksheet?
Use the area sheet before the perimeter sheet so students see why the straight sides matter. Semicircle and Quarter Circle Review checks every skill with an Answer Bank.
What students will practice
- Students will find the area of a semicircle by halving the area of a full circle.
- Students will find the area of a quarter circle by dividing a circle's area by 4.
- Students will change a diameter to a radius before using A = πr².
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FAQ
How do I use this semicircles and quarter circles worksheet?
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Use the area sheet before the perimeter sheet so students see why the straight sides matter. Semicircle and Quarter Circle Review checks every skill with an Answer Bank.
What does this worksheet teach?
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Find the area of 12 semicircles and quarter circles from a radius or diameter, such as d = 12 cm. The directions on the page read: Find the area A of each semicircle or quarter circle. Use 3.14 for π, round to the nearest tenth and include square units. The page opens with a worked example, and an answer key is included.
Can I use this semicircles and quarter circles worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade geometry, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
How do you find the area of a semicircle?
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Find the area of the full circle with A = πr², then divide by 2. A semicircle with a 13 cm diameter has a radius of 6.5 cm, so its area is about 66.3 cm². For a quarter circle, divide by 4 instead.
How do you find the perimeter of a quarter circle?
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Find the curved arc, which is one fourth of the full circumference, then add the two radii. For r = 17 cm the arc is about 26.7 cm, so the perimeter is about 60.7 cm. Perimeter of Semicircles and Quarter Circles practices this on 12 figures.
Why is the perimeter of a semicircle not just half the circumference?
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Half the circumference is only the curved part. The perimeter also includes the straight diameter across the bottom. A semicircle with r = 15 cm has a perimeter of (15π + 30) cm.
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