Question

find the area of the shaded region. (assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit. assume a = 3 ft, b = 6 ft, c = 11 ft, and d = 14 ft.)

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=b\times d\). Substituting \(b = 6\) ft and \(d=14\) ft, we get \(A_{rectangle}=6\times14 = 84\) \(ft^{2}\).

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}\times a\times d\). Substituting \(a = 3\) ft and \(d = 14\) ft, we get \(A_{triangle}=\frac{1}{2}\times3\times14=21\) \(ft^{2}\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A\) is the sum of the area of the rectangle and the area of the triangle. So \(A=A_{rectangle}+A_{triangle}\). Substituting the values from Step1 and Step2, we have \(A = 84+21=105\) \(ft^{2}\).

Answer:

\(105\)