There are two different shapes in the iamge, the first is a rectangle and the second is a triangle. To determine the area of each of these, we need to use the following expressions:
[tex]\begin{gathered} A_{\text{square}}=side^2 \\ A_{triangle}=\frac{b\cdot h}{2} \end{gathered}[/tex]
Since there are two triangles, the total area of the image is:
[tex]A=A_{\text{square}}+2\cdot A_{\text{triangle}}[/tex]
So we need to calculate the area of each shape first. This is done below:
[tex]\begin{gathered} A_{\text{square}}=4.5^2=20.25\text{ square inches} \\ A_{\text{triangle}}=\frac{4.5\cdot6}{2}=13.5\text{ square inches} \end{gathered}[/tex]
Now we can calculate the total area:
[tex]A=20.25+2\cdot13.5=47.25\text{ square inches}[/tex]
The total area is 47.25 square inches
