Question

1. What is the total area of this figure? How to calculate it?

Answer 1

Given the figure shown in the exercise, you can identify that it is formed by a triangle and a rectangle. Then, the total area of the figure will be the sum of the area of the triangle and the area of the rectangle.

• The formula for calculating the area of a rectangle is:

`A_r=lw`

Where "l" is the length and "w" is the width.

In this case:

`\begin{gathered} l=8ft \\ w=2ft \end{gathered}`

Then, by substituting the values into the formula and evaluating, you get:

`A_r=\left(8ft\right)\left(2ft\right)=16ft^2`

• The formula for calculating the area of a triangle is:

`A_t=(bh)/(2)`

Where "b" is the base and "h" is the height of the triangle.

In this case, you can identify that:

`\begin{gathered} b=8ft \\ h=16ft-2ft=14ft \end{gathered}`

See the picture below:

Knowing the base and the height of the triangle, you can substitute values into the formula and evaluate, in order to find its area:

`A_t=(\left(8ft\right)\left(14ft\right))/(2)=(112ft^2)/(2)=56ft^2`

Therefore, you can determine that the total area of the figure is:

`\begin{gathered} A_(total)=16ft^2+56ft^2 \\ \\ A_(total)=72ft^2 \end{gathered}`

Hence, the answer is:

`A_(total)=72ft^2`