Question

find the area of the geometric figure. the area is \boxed{} (simplify your answer.) this quiz: 34 point(s) possible this question: 1 point(s) possible logic and geometry 4 of 34 submit (triangle with base $9\frac{1}{2}$ yd and height 7 yd)

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

The base of the triangle is \( 9\frac{1}{2} \) yd, which is equal to \( \frac{19}{2} \) yd (since \( 9\frac{1}{2} = \frac{9\times2 + 1}{2} = \frac{19}{2} \)), and the height is \( 7 \) yd.

Step3: Substitute the values into the formula

Substitute the base \( \frac{19}{2} \) yd and height \( 7 \) yd into the formula:
\[
A = \frac{1}{2} \times \frac{19}{2} \times 7
\]

Step4: Calculate the area

First, multiply \( \frac{1}{2} \) and \( \frac{19}{2} \) to get \( \frac{19}{4} \), then multiply by \( 7 \):
\[
A = \frac{19}{4} \times 7 = \frac{133}{4} = 33\frac{1}{4}
\]

Answer:

\( 33\frac{1}{4} \) square yards (or \( \frac{133}{4} \) square yards)