Question

find the area of the geometric figure. image: triangle with base (9\frac{1}{2}) yd and height 3 yd the area is (square) (\boldsymbol{
abla}). (simplify your answer.)

Explanation:

Step1: Recall the formula for the area of a triangle

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

Step2: Identify the base and height

From the figure, the base of the triangle is \( 9\frac{1}{2} \) yd (which is \( \frac{19}{2} \) yd as an improper fraction) and the height is \( 3 \) yd.

Step3: Substitute the values into the formula

\[

$$\begin{align*} A&=\frac{1}{2}\times\frac{19}{2}\times3\\ &=\frac{1\times19\times3}{2\times2}\\ &=\frac{57}{4}\\ & = 14\frac{1}{4} \end{align*}$$

\]

Answer:

\( 14\frac{1}{4} \) square yards (or \( \frac{57}{4} \) square yards)