M16 | Maths Made Easy

# M16

## Question: Shapes A and B are similar. Work out the area of shape A.

Answer: Firstly, we will determine the scale factor that relates the side-lengths by dividing the side-length of the bigger shape by that of the smaller shape: $SF=28\div7=4$.

Now, if the scale factor for the side-lengths is 4, then that means that the scale factor for the areas is: $SF_A=4^2=16$.

Therefore, to find the area of the smaller shape, we need to divide the area of the bigger shape by the area scale factor: 16. Doing so, we get

$\text{Area of A }=320\div16=20\text{ cm}^2$.