Question

what is the area of the shaded region?
34.9 ft
22.5 ft
23.8 ft
34.2 ft
write your answer as a whole number or a decimal rounded to the nearest hundredth.

Explanation:

Step1: Calculate area of large triangle

The formula for the area of a triangle is $A = \frac{1}{2} \times base \times height$. For the large triangle, base = 34.9 ft and height = 34.2 ft. So, $A_{large} = \frac{1}{2} \times 34.9 \times 34.2$.
$A_{large} = \frac{34.9 \times 34.2}{2} = \frac{1193.58}{2} = 596.79$ square feet.

Step2: Calculate area of small triangle

For the small triangle, base = 22.5 ft and height = 23.8 ft. Using the same formula, $A_{small} = \frac{1}{2} \times 22.5 \times 23.8$.
$A_{small} = \frac{22.5 \times 23.8}{2} = \frac{535.5}{2} = 267.75$ square feet.

Step3: Subtract small area from large area

The area of the shaded region is $A_{shaded} = A_{large} - A_{small}$.
$A_{shaded} = 596.79 - 267.75 = 329.04$ square feet.

Answer:

329.04