Question

what is the area of the shaded region?
71 mm
71 mm
43 mm
43 mm
write your answer as a whole number or a decimal rounded to the nearest hundredth.
square millimeters

Explanation:

Step1: Calculate area of large triangle

The formula for the area of a right triangle is $A = \frac{1}{2} \times base \times height$. For the large triangle, base = 71 mm and height = 71 mm. So, $A_{large} = \frac{1}{2} \times 71 \times 71$.
$A_{large} = \frac{1}{2} \times 5041 = 2520.5$ square millimeters.

Step2: Calculate area of small triangle

For the small triangle, base = 43 mm and height = 43 mm. Using the same formula, $A_{small} = \frac{1}{2} \times 43 \times 43$.
$A_{small} = \frac{1}{2} \times 1849 = 924.5$ square millimeters.

Step3: Subtract areas to find shaded region

The area of the shaded region is $A_{shaded} = A_{large} - A_{small}$.
$A_{shaded} = 2520.5 - 924.5 = 1596$ square millimeters.

Answer:

1596