Question

find the area of the triangle shown below.
( 2\frac{3}{5} ) yd
( 2 ) yd (dashed, right angle)
( 5 ) yd
( 3\frac{9}{10} ) yd
note: figure may not be drawn to scale.
label required

Explanation:

Step1: Recall the formula for the area of a triangle

The area \( A \) of a triangle is given by \( A=\frac{1}{2}\times\text{base}\times\text{height} \). Here, the base of the triangle is \( 5 \) yd and the height (the perpendicular distance from the opposite vertex to the base) is \( 2 \) yd.

Step2: Substitute the values into the formula

Substitute base \( = 5 \) yd and height \( = 2 \) yd into the formula:
\( A=\frac{1}{2}\times5\times2 \)

Step3: Simplify the expression

First, multiply \( 5 \) and \( 2 \): \( 5\times2 = 10 \). Then, multiply by \( \frac{1}{2} \): \( \frac{1}{2}\times10=5 \).

Answer:

The area of the triangle is \( 5 \) square yards (or \( 5\ \text{yd}^2 \)).