Question

find the area of the geometric figure. the area is \boxed{} (simplify your answer.) (the geometric figure is a triangle with base (6\frac{1}{2}) yd and height 5 yd, as shown in the image.)

Explanation:

Step1: Recall triangle area formula

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

Step2: Identify base and height

The base of the triangle is \( 6\frac{1}{2} \) yd (which is \( \frac{13}{2} \) yd) and the height is 5 yd.

Step3: Substitute into formula

Substitute the values into the formula: \( A = \frac{1}{2} \times \frac{13}{2} \times 5 \).

Step4: Calculate the area

First, multiply \( \frac{1}{2} \) and \( \frac{13}{2} \) to get \( \frac{13}{4} \), then multiply by 5: \( \frac{13}{4} \times 5 = \frac{65}{4} = 16\frac{1}{4} \) square yards.

Answer:

\( 16\frac{1}{4} \) square yards (or \( \frac{65}{4} \) square yards)