Question

Sammy finds satellite images of a school and a museum. They put the images on a coordinate grid (shown below). Compare the area of the school and the museum.

Answer 1

The area of the museum is given by:

`\begin{gathered} A=\pi r^2 \\ \text{Where:} \\ r=30m \\ A=\pi(30^2)=900\pi\approx2827m^2 \end{gathered}`

The area of the school is:

`\begin{gathered} A=w\cdot l \\ \text{where:} \\ w=\text{width} \\ l=\text{length} \\ w=\sqrt[]{30^2+10^2}=10\sqrt[]{10} \\ l=\sqrt[]{60^2+20^2}=20\sqrt[]{10} \\ A=(10\sqrt[]{10})(20\sqrt[]{10})=2000m^2 \end{gathered}`
`2827m^2-2000m^2=827m^2`

The area of the school is about 827m² less than the area of the museum