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 area of triangle

The formula for the area of a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, the base is $8m$ and the height is $(5 + 2)=7m$. So, $A_{triangle}=\frac{1}{2}\times8\times7 = 28m^{2}$.

Step2: Calculate area of rectangle

The formula for the area of a rectangle is $A_{rectangle}=length\times width$. Here, the length is $2m$ and the width is $1m$. So, $A_{rectangle}=2\times1 = 2m^{2}$.

Step3: Calculate area of shaded region

The area of the shaded region $A$ is the area of the triangle minus the area of the rectangle. So, $A = A_{triangle}-A_{rectangle}=28 - 2=26m^{2}$.

Answer:

$26m^{2}$