Question

what is the area?
write your answer as a fraction or as a whole or mixed number.
triangle image with height (2\frac{3}{4}) ft and base (2\frac{4}{5}) ft
(square) square feet
submit

Explanation:

Step1: Recall the formula for the area of a triangle

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

Step2: Convert mixed numbers to improper fractions

Convert \( 2\frac{4}{5} \) to an improper fraction: \( 2\frac{4}{5}=\frac{2\times5 + 4}{5}=\frac{14}{5} \).
Convert \( 2\frac{3}{4} \) to an improper fraction: \( 2\frac{3}{4}=\frac{2\times4+3}{4}=\frac{11}{4} \).

Step3: Substitute into the area formula

Substitute base \( \frac{14}{5} \) and height \( \frac{11}{4} \) into \( A = \frac{1}{2}\times\text{base}\times\text{height} \):
\( A=\frac{1}{2}\times\frac{14}{5}\times\frac{11}{4} \).

Step4: Simplify the expression

First, simplify \( \frac{1}{2}\times\frac{14}{5}=\frac{7}{5} \). Then, multiply by \( \frac{11}{4} \): \( \frac{7}{5}\times\frac{11}{4}=\frac{77}{20} \).
Convert \( \frac{77}{20} \) to a mixed number: \( \frac{77}{20}=3\frac{17}{20} \).

Answer:

\( 3\frac{17}{20} \)