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 area formula for a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, base = 8 cm and height = 8 cm. So $A_{triangle}=\frac{1}{2}\times8\times8 = 32$ $cm^{2}$.

Step2: Calculate area of rectangle

The area formula for a rectangle is $A_{rectangle}=length\times width$. Here, length = 3 cm and width = 2 cm. So $A_{rectangle}=3\times2=6$ $cm^{2}$.

Step3: Calculate area of shaded region

The area of the shaded region is the area of the triangle minus the area of the rectangle. So $A = A_{triangle}-A_{rectangle}=32 - 6=26$ $cm^{2}$.

Answer:

$26$ $cm^{2}$