Question

what is the area of the composite figure?
image of composite figure with dimensions: 5 in. (height of left rectangle), 5 in. (width of left rectangle), 15 in. (total width), 10 in. (height of right part)
a) 100 square inches
b) 137½ square inches
c) 150 square inches
d) 175 square inches

Explanation:

Step1: Split into rectangle + trapezoid

Divide the composite figure into a 5in×5in rectangle and a trapezoid with bases 5in, 10in, height \(15-5=10\) in.

Step2: Calculate rectangle area

Area = \(5 \times 5 = 25\) square inches

Step3: Calculate trapezoid area

Use formula \(A=\frac{1}{2}(b_1+b_2)h\):
\(A=\frac{1}{2}(5+10) \times 10 = 75\) square inches

Step4: Sum the two areas

Total area = \(25 + 75 = 100\) square inches

Answer:

A. 100 square inches