A semicircle is half a circle and a quarter circle is a quarter of one, so the area is easy: work out the whole circle, then divide by 2 or by 4. The perimeter is where the marks go. Cutting a circle in half opens up a straight edge, so a semicircle's perimeter is the curved arc PLUS the diameter — it is not half the circumference. A quarter circle closes with two straight radii instead. Always do the whole circle first, then divide, then add the straight edges back on.
Worked example
Problem A semicircle has a radius of 7 cm. Take π = 22/7. Find its area and its perimeter.
Whole circle first: area = 22/7 × 7 × 7 = 154 cm².
A semicircle is half of that: 154 ÷ 2 = 77 cm².
For the perimeter, the curved edge is half the circumference: π × r = 22/7 × 7 = 22 cm.
Now add the straight edge, which is the diameter 7 × 2 = 14 cm: 22 + 14 = 36 cm.
Watch out Half the circumference is 22 cm, but the perimeter is 36 cm. The straight edge is part of the boundary — leaving it out is the single commonest error in this lesson.