Question

what is the area?
write your answer as a fraction or as a whole or mixed number.
$7\frac{1}{2}$ ft
$9\frac{2}{3}$ ft
\boxed{} square feet
submit

Explanation:

Step1: Recall the formula for the area of a triangle

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

Step2: Convert the mixed numbers to improper fractions

The height $h = 7\frac{1}{2}=\frac{7\times2 + 1}{2}=\frac{15}{2}$ ft and the base $b = 9\frac{2}{3}=\frac{9\times3+ 2}{3}=\frac{29}{3}$ ft.

Step3: Substitute into the area formula

$A=\frac{1}{2}\times\frac{29}{3}\times\frac{15}{2}$
First, simplify $\frac{15}{2}$ and $\frac{1}{2}$ (or multiply the numerators and denominators directly). $\frac{1}{2}\times\frac{15}{2}=\frac{15}{4}$, then $\frac{15}{4}\times\frac{29}{3}=\frac{15\times29}{4\times3}=\frac{435}{12}$.

Step4: Simplify the fraction

Simplify $\frac{435}{12}$: divide numerator and denominator by 3, we get $\frac{145}{4}$. Convert $\frac{145}{4}$ to a mixed number: $145\div4 = 36$ with a remainder of 1, so $\frac{145}{4}=36\frac{1}{4}$.

Answer:

$36\frac{1}{4}$