The circle

The perimeter of a semicircle

Remember that the perimeter is the distance round the outside.

A semicircle has two edges. One is half of a circumference and the other is a diameter.

Diagram of a semicircle with an 8cm diameter

\[C = \pi d\]

\[= 3.14 \times 8\]

\[= 25.12cm\]

Remember this is the circumference of the whole circle, so now we need to half this answer.

\[25.12 \div 2 = 12.56cm\]

Total perimeter \(= 12.56 + 8 = 20.56cm\)

Area of a circle

For any circle with radius, r, the area, A, is found using the formula:

\[A = \pi {r^2}\]

Diagram of a circle with a radius of 12cm

\[A = \pi {r^2}\]

\[= 3.14 \times 12 \times 12\]

\[= 452.16c{m^2}\]

The area of a semicircle

A semicircle is just half of a circle. To find the area of a semicircle we calculate the area of the whole circle and then half the answer.

Diagram of a semicircle with an 4cm diameter

\[A = \pi {r^2}\]

\[= 3.14 \times 4 \times 4\]

\[= 50.24c{m^2}\]

Area of semicircle \(= 50.24 \div 2 = 25.12c{m^2}\)

The area of a combined shape

This shape is made up of a rectangle and a semicircle.

To find the total area we just find the area of each part and add them together.

Combined rectangle and semicircle measuring 20mm x 30mm

Area of the rectangle = length x breadth

\[= 20 \times 30\]

\[= 600m{m^2}\]

\[Area\,of\,circle = \pi {r^2}\]

\[= 3.14 \times 10 \times 10\]

\[= 314m{m^2}\]

\[Area\,of\,semicircle = 314 \div 2 = 157m{m^2}\]

\[Total\,area = 600 + 157\]

\[= 757m{m^2}\]