Question

which value is closest to the area of the following figure, in square inches? 8 in 8 in 9 in 9 in 12 in 8 in 8 in 86 in² 64 in² 108 in² 74 in²

Explanation:

Step1: Divide the figure

The figure can be divided into a rectangle and a right - triangle. The rectangle has length $l = 16$ inches and width $w = 9$ inches, and the right - triangle has base $b=8$ inches and height $h = 9$ inches.

Step2: Calculate rectangle area

The area formula for a rectangle is $A_{rect}=l\times w$. Here, $l = 16$ inches and $w = 9$ inches, so $A_{rect}=16\times9=144$ square inches. But this is wrong. Let's correct. The rectangle has length $l = 8$ inches and width $w = 9$ inches, so $A_{rect}=8\times9 = 72$ square inches.

Step3: Calculate triangle area

The area formula for a triangle is $A_{tri}=\frac{1}{2}\times b\times h$. Here, $b = 8$ inches and $h = 9$ inches, so $A_{tri}=\frac{1}{2}\times8\times9=36$ square inches.

Step4: Calculate total area

The total area of the figure $A = A_{rect}+A_{tri}$. Substitute the values: $A=72 + 36=108$ square inches.

Answer:

$108$ in$^{2}$