Question

what is the area of this figure?
write your answer using decimals, if necessary.
square inches

Explanation:

Step1: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 9\) in and \(h=8 + 5+2=15\) in.

$$ A_{triangle}=\frac{1}{2}\times9\times15=\frac{135}{2}=67.5 $$

Step2: Calculate the area of the middle rectangle

The formula for the area of a rectangle is \(A = lw\). Here, \(l = 5\) in and \(w = 2\) in.

$$ A_{middle - rectangle}=5\times2 = 10 $$

Step3: Calculate the area of the bottom - right rectangle

First, find the length of the bottom - right rectangle. The total length of the base of the figure (from the left - most point to the right - most point) can be found by considering the horizontal segments. The base of the triangle is \(9\) in, and then we have a \(2\) - in segment and an \(8\) - in segment. The width of the bottom - right rectangle is \(2\) in. The length of the bottom - right rectangle: we know that if we consider the horizontal lengths, the length \(l=(9 + 2+8)-(2 + 6)=11\) in (by subtracting the non - contributing horizontal segments). Using \(A=lw\) with \(l = 11\) in and \(w = 2\) in.

$$ A_{bottom - right - rectangle}=11\times2=22 $$

Step4: Sum up the areas

$$ A=A_{triangle}+A_{middle - rectangle}+A_{bottom - right - rectangle}=67.5+10 + 22 $$

$$ A=99.5 $$

Answer:

\(99.5\)