Question

the shaded triangle has an area of $16\\ \text{in}^2$.
find the area of the entire rectangle.
be sure to include the correct unit in your answer.

Explanation:

Step1: Recall triangle and rectangle area relation

For a rectangle with length \( l \) and width \( w \), the area of the rectangle is \( A_{rectangle}=l\times w \). The shaded triangle has a base equal to the length of the rectangle and height equal to the width of the rectangle. The area of a triangle is \( A_{triangle}=\frac{1}{2}\times base\times height \). So, \( A_{triangle}=\frac{1}{2}\times A_{rectangle} \).

Step2: Solve for rectangle area

Given \( A_{triangle} = 16\space in^2 \), and \( A_{triangle}=\frac{1}{2}\times A_{rectangle} \), we can rearrange to find \( A_{rectangle}=2\times A_{triangle} \). Substituting the value of the triangle's area, we get \( A_{rectangle}=2\times16 \).
\( A_{rectangle}=32\space in^2 \)

Answer:

\( 32 \) square inches