Question

a rectangle is removed from a right triangle to create the shaded region shown below. find the area of the shaded region. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the area of the right - triangle

The formula for the area of a right - triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base is \(8m\) and the height is \(10m\).
\(A_{triangle}=\frac{1}{2}\times8\times10 = 40m^{2}\)

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = length\times width\). Here, the length is \(3m\) and the width is \(2m\).
\(A_{rectangle}=3\times2=6m^{2}\)

Step3: Calculate the area of the shaded region

The area of the shaded region is the area of the triangle minus the area of the rectangle.
\(A = A_{triangle}-A_{rectangle}\)
\(A=40 - 6=34m^{2}\)

Answer:

\(34m^{2}\)