Question

the entire rectangle below has an area of $52\\ \text{ft}^2$. find the area of the shaded triangle. be sure to include the correct unit in your answer.

Explanation:

Step1: Recall the relationship between the area of a rectangle and a triangle with the same base and height.

The area of a rectangle is given by \( A_{rectangle} = length \times width \). For a triangle that shares the same base and height as the rectangle (like the shaded triangle here, where the base is the length of the rectangle and the height is the width of the rectangle), the area of the triangle is \( A_{triangle}=\frac{1}{2}\times base\times height \). Since \( A_{rectangle}=base\times height \), the area of the triangle is half of the area of the rectangle.

Step2: Calculate the area of the shaded triangle.

Given the area of the rectangle is \( 52\space ft^{2} \), the area of the shaded triangle is \( \frac{52}{2} \).
\( \frac{52}{2}=26 \)

Answer:

\( 26\space square\space feet \) (or \( 26\space ft^{2} \))