Question

what is the area?
write your answer as a fraction or as a whole or mixed number.
(image of a triangle with height 5 1/4 yd and base 3 3/5 yd)
square yards
submit

Explanation:

Step1: Recall triangle area formula

The area of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Here, the base is \( 3\frac{3}{5} \) yd and the height is \( 5\frac{1}{4} \) yd.

Step2: Convert mixed numbers to improper fractions

Convert \( 3\frac{3}{5} \) to an improper fraction: \( 3\frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{18}{5} \).
Convert \( 5\frac{1}{4} \) to an improper fraction: \( 5\frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4} \).

Step3: Substitute into the area formula

Substitute base \( \frac{18}{5} \) and height \( \frac{21}{4} \) into \( A = \frac{1}{2} \times \text{base} \times \text{height} \):
\( A = \frac{1}{2} \times \frac{18}{5} \times \frac{21}{4} \).

Step4: Simplify the expression

First, multiply \( \frac{18}{5} \times \frac{21}{4} = \frac{18 \times 21}{5 \times 4} = \frac{378}{20} \).
Then, multiply by \( \frac{1}{2} \): \( \frac{1}{2} \times \frac{378}{20} = \frac{378}{40} \).
Simplify \( \frac{378}{40} \) by dividing numerator and denominator by 2: \( \frac{189}{20} \).
Convert \( \frac{189}{20} \) to a mixed number: \( 9\frac{9}{20} \).

Answer:

\( 9\frac{9}{20} \)