Semicircle Answers in Terms of Pi

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.

Find the area and perimeter of 12 semicircles and quarter circles in terms of π, such as (15π + 30) cm. The directions on the page read: Find the area A and the perimeter P of each figure. Leave answers in terms of π, for example 2.5π cm² and (3π + 11) cm. Include units. The page opens with a worked example, and an answer key is included.

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.

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.

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.

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.