Geometric skillsThe circle

Various formulae are used to calculate perimeter, area or volume. The order of rotational symmetry is how many times a shape fits into its original shape during a rotation of 360 degrees.

Part ofMathsGeometry

The circle

The of a semi circle 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 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

\(= 20 \times 30\)

\(= 600m{m^2}\)

\(Area\,of\,circle = \pi {r^2}\)

\(= 3.14 \times 10 \times 10\)

\(= 314m{m^2}\)

\(Area\,of\,semicircle = 314 \div 2 = 157m{m^2}\)

\(Total\,area = 600 + 157\)

\(= 757m{m^2}\)