Question

find the area of the geometric figure. the area is □. (simplify your answer.) (the geometric figure is a triangle with base ( 8\frac{1}{2} ) yd and height 3 yd, as shown in the image.)

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \( A=\frac{1}{2}\times\text{base}\times\text{height} \).

Step2: Identify the base and height

From the figure, the base of the triangle is \( 8\frac{1}{2}\text{ yd} \) (which is \( \frac{17}{2}\text{ yd} \)) and the height is \( 3\text{ yd} \).

Step3: Substitute the values into the formula

Substitute base \( b = \frac{17}{2} \) and height \( h = 3 \) into the formula:
\( A=\frac{1}{2}\times\frac{17}{2}\times3 \)

Step4: Calculate the area

First, multiply \( \frac{1}{2} \) and \( \frac{17}{2} \) to get \( \frac{17}{4} \), then multiply by 3:
\( A=\frac{17\times3}{4}=\frac{51}{4}=12\frac{3}{4}\text{ square yards} \) (or \( 12.75 \) square yards)

Answer:

\( 12\frac{3}{4} \) (or \( 12.75 \)) square yards