Question

A figure is made up of a triangle and a square. The square andthe triangle have the same base of 9 inches. The triangle has aheight of 7 inches, what is the total area of the figure?

Answer 1

To solve the exercise, it is helpful first to draw the situation that the statement describes:

The total area of ​​the figure will be

`A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}}`

Then, we can calculate the area of ​​the square using the following formula:

`\begin{gathered} A_{\text{square}}=s\cdot s \\ \text{ Where s is one side of the square} \end{gathered}`

So, we have:

`\begin{gathered} s=9in \\ A_{\text{square}}=s\cdot s \\ A_{\text{square}}=9in\cdot9in \\ \boldsymbol{A}_{\boldsymbol{square}}\boldsymbol{=81in}^{\boldsymbol{2}} \end{gathered}`

Now, we can calculate the area of the triangle using the following formula:

`\begin{gathered} A_{\text{triangle}}=(b\cdot h)/(2) \\ \text{ Where b is the base and} \\ h\text{ is the height of the triangle} \end{gathered}`

So, we have:

`\begin{gathered} b=9in \\ h=7in \\ A_{\text{triangle}}=(b\cdot h)/(2) \\ A_{\text{triangle}}=(9in\cdot7in)/(2) \\ A_{\text{triangle}}=(63in^2)/(2) \\ \boldsymbol{A}_{\boldsymbol{triangle}}\boldsymbol{=31.5in}^{\boldsymbol{2}} \end{gathered}`

Finally, we calculate the total area of ​​the figure

`\begin{gathered} A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}} \\ A_{\text{total}}=81in^2+31.5in^2 \\ \boldsymbol{A}_{\boldsymbol{total}}\boldsymbol{=112.5in}^{\boldsymbol{2}} \end{gathered}`

Therefore, the total area of the figure is 112.5 square inches, and the correct answer is option C.