Question

find the area of the shaded region below. (assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit.)

Explanation:

Step1: Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A = base\times height\). Here, the base \(b = 15\) mm and the height \(h=10\) mm.
\(A_{parallelogram}=15\times10 = 150\) \(mm^{2}\)

Step2: Calculate the area of the un - shaded triangle

The base of the triangle \(b_{triangle}=19 - 18=1\) mm and the height \(h_{triangle}=10\) mm. The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).
\(A_{triangle}=\frac{1}{2}\times1\times10 = 5\) \(mm^{2}\)

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{parallelogram}-A_{triangle}\)
\(A=150 - 5=145\) \(mm^{2}\)

Answer:

\(145\)