IGCSE Maths / Circles, cylinders, cones and spheres

Semicircles: perimeter and area

Edexcel International GCSE Maths (4MA1), chapter 12: Circles, cylinders, cones and spheres, specification point 4.9e-f. Free lesson.

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A semicircle has half the area and half the circumference of its full circle. To find its perimeter, add the straight diameter to the curved edge.

The diameter and radius

The diameter goes right across a circle through its centre. It is twice the radius, and both circle formulae use the radius. So, if a question gives you the diameter, halve it first. d = 2r r = d/2 Putting the diameter into a formula that needs r can make the answer too large. For area, it makes the answer four times too big.

The two circle formulae

A semicircle comes from cutting a circle in half, so begin with the formulae for a whole circle. Circumference measures the distance around the edge. Area measures the space inside. These formulae need to be learnt. Circumference: C = 2πr, measured in units such as cm. Area: A = πr², measured in square units such as cm². Half the circumference is the semicircle's curved edge: 1/2 × 2πr = πr. Half the area is the semicircle's area: 1/2πr².

Find a semicircle's curved edge and area

A semicircle is half of a full circle, so use half of the relevant circle formula. Keep curved edge and area separate: one is a length and the other is a space measurement.

Find the perimeter

The perimeter is the whole distance around the outside. A semicircle has a curved edge and a straight edge across the middle, so its perimeter is not just half the circumference. Perimeter = curved edge + diameter. If the diameter is given, find the radius before using the circumference formula.

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