Question

what is the area of the shaded region? 73 mi 52 mi 57 mi 91 mi 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 = 73 mi, height = 91 mi.
$A_{large} = \frac{1}{2} \times 73 \times 91$
$A_{large} = \frac{73\times91}{2} = \frac{6643}{2} = 3321.5$ square miles.

Step2: Calculate area of small triangle

For the small triangle, base = 52 mi, height = 57 mi.
$A_{small} = \frac{1}{2} \times 52 \times 57$
$A_{small} = \frac{52\times57}{2} = 26\times57 = 1482$ square miles.

Step3: Find area of shaded region

Subtract the area of the small triangle from the large triangle.
$A_{shaded} = A_{large} - A_{small}$
$A_{shaded} = 3321.5 - 1482 = 1839.5$

Answer:

1839.5