Question

marys backyard has a patio and a garden. find the area of the garden. (sides meet at right angles.)

Explanation:

Step1: Calculate the area of the larger rectangle

The formula for the area of a rectangle is \(A = l\times w\). The length of the larger rectangle (garden + part of the patio) is \(3 + 2=5\) yards and the width is \(4 + 2 = 6\) yards. So the area \(A_1=(3 + 2)\times(4 + 2)=5\times6 = 30\) square yards.

Step2: Calculate the area of the patio

The patio has length \(3\) yards and width \(2\) yards. Using the area formula \(A = l\times w\), the area of the patio \(A_2=3\times2=6\) square yards.

Step3: Calculate the area of the garden

Subtract the area of the patio from the area of the larger rectangle. \(A = A_1 - A_2\). So \(A=30- 6=24\) square yards.

Answer:

\(24\)