M3 | Maths Made Easy

# M3

Question: A shape ABCD is made from a rectangle and a semicircle as shown. Calculate the perimeter to 1 decimal place.

Answer: We can see that the side lengths of the rectangle are 4cm and 6cm… however it’s not immediately clear how to get the length of the curved edge joining A and B!

We can work this out using the formula for the circumference of a circle, $c=\pi d$. We can see the diameter of the circle is 4cm, the same as the length of the shortest edge of the rectangle. The circumference of a circle with a diameter of 4cm would be 4$\pi$. However we only have half a circumference here, so the length of the curved edge is 2$\pi$. This means the total perimeter of the shape is:

$6+4+6+2\pi =22.3$ (1 d.p.)