Question

find the area of the geometric figure. image of triangle with height 5 yd and base 8\frac{1}{2} yd the area is \square cubic yards. (simplify your answer.)

Explanation:

Step1: Recall the area formula for a triangle

The area \( A \) of a triangle is given by \( A=\frac{1}{2}\times\text{base}\times\text{height} \). Here, the base is \( 8\frac{1}{2} \) yd (which is \( \frac{17}{2} \) yd) and the height is \( 5 \) yd.

Step2: Substitute the values into the formula

\( A = \frac{1}{2}\times\frac{17}{2}\times5 \)
First, multiply \( \frac{1}{2} \) and \( \frac{17}{2} \): \( \frac{1\times17}{2\times2}=\frac{17}{4} \)
Then multiply by \( 5 \): \( \frac{17}{4}\times5=\frac{85}{4}=21\frac{1}{4} \) (or \( 21.25 \)) square yards (note: area is in square units, not cubic).

Answer:

\( 21\frac{1}{4} \) (or \( 21.25 \)) square yards