ShapesProperties
- Its area is half the area of the full circle.
- Its curved edge is half the circumference.
- Any angle drawn in a semicircle, with its corner on the curve and its arms to the ends of the diameter, is a right angle.
- It has one line of symmetry.
Why the formulas work
Half a circle has half the area: ½πr². The perimeter needs care. The curved edge is half the circumference, πr, but the shape is closed by the diameter as well, which adds 2r. So the perimeter is πr + 2r, not just πr.
Worked example
Take a semicircle with radius 7 cm.
- Area. Area = ½ πr2. Here: ½ × π × 7 × 7 = 76.97 cm² (with π = 22/7: 77 cm²).
- Curved edge. Curved edge = πr. Here: π × 7 = 21.99 cm (with π = 22/7: 22 cm).
- Perimeter. Perimeter = πr + 2r. Here: π × 7 + 2 × 7 = 35.99 cm (with π = 22/7: 36 cm).
Finding a missing measurement
From the perimeter, r = P ÷ (π + 2). With π = 22/7 that is P × 7 ÷ 36, so a perimeter of 72 cm gives r = 14 cm. From the area, r = √(2A ÷ π): an area of 77 cm² gives r² = 49, so r = 7 cm.
Mistakes to avoid
- Leaving out the diameter when asked for the perimeter.
- Halving the radius. Only the area and the curve are halved, not r.
Where you see it
A protractor, a hand fan opened fully, arches over doors and windows, and a slice of watermelon are semicircles.
Try these
Work each one out, then tap to check.
A semicircle has radius 14 cm. Find its area, curved edge and perimeter. Take π = 22/7.
Area = 308 cm²; Curved edge = 44 cm; Perimeter = 72 cm.
A semicircle has radius 3.5 cm. Find its area, curved edge and perimeter. Take π = 22/7.
Area = 19.25 cm²; Curved edge = 11 cm; Perimeter = 18 cm.