Question

A path2mwide surroundings a rectangular garden 20mlong and 12mwide. Find the area of the path.

Short answer

The area of the path is $144m^2.$

Step-by-step solution

Step 1. Given information.

Length of the garden$=20m$

Width of the garden $=12m$

Width of the path$=2m$

Step 2. Concept  Used.

If b is the base of the reactangle and h is the height of the rectangle.

Then, the area of the rectangle is$A=b\times h$

Step 3. Let’s calculate the area of the path.

In$▱PQRS$where,

Length=$(20+2+2)=24m$

Width=$(12+2+2)=16m$

Put the value of length and width into the formula and find the area.

Area of the$▱PQRS$:$\begin{array}{c}{A}_1=24\times 16\\ =384m^2\end{array}$

Now,$▱ABCD$

Inwhere,

Length=$20m$

Width=$12m$

Put the value of length and width into the formula and find the area.

Area of the$▱ABCD$:

$\begin{array}{c}{A}_2=20\times 12\\ =240m^2\end{array}$

Now,

The area of the path = Area of the rectangle PQRS-Area of the rectangle ABCD

$\begin{array}{c}A=(384-240)\\ =144c{m}^2\end{array}$

Therefore, the area of the path is$144c{m}^2.$