what is the area of this figure?\nwrite your answer using decimals, if necessary.\nsquare 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)