Question

Find the perimeter and area of the figure pictured below.

8m
4m
Perimeter =
Area =
12 m
2m
m²
2
m
Q.

Answer 1

Perimeter = 40 m

Area = 48 m²

Explanation:

The perimeter of a two-dimensional figure is the sum of all its sides.

Therefore, the perimeter of the given figure can be calculated as follows:

`\begin{aligned}\textsf{Perimeter}&=2 + 12 + 8 + 4 + (8 - 2) + (12 - 4)\\&=2+12+8+4+6+8\\&=14+8+4+6+8\\&=22+4+6+8\\&=26+6+8\\&=32+8\\&=40\; \sf m \end{aligned}`

So, the perimeter of the given figure is 40 m.

To calculate the area of the figure, we can separate the figure into two rectangles (see attachment). The area of a rectangle is the product of its width and length. Therefore:

`\begin{aligned}\sf Area&=\sf Area_(\sf Rectangle\;1)+Area_(\sf Rectangle\;2)\\&=(4 * 8)+(2* (12-4))\\&=(4 * 8)+(2* 8)\\&=32+16\\&=48\; \sf m^2\end{aligned}`

So, the area of the given figure is 48 m².