Question

what is the area of this figure?
if necessary, round your answer to the nearest hundredth.
square kilometers

Explanation:

Step1: Split figure into 3 parts

Divide the shape into a quarter-circle, a large rectangle, and a small rectangle.

Step2: Calculate quarter-circle area

Radius $r = 10$ km. Area formula: $\frac{1}{4} \pi r^2$
$\frac{1}{4} \times \pi \times 10^2 = 25\pi \approx 78.54$ km²

Step3: Calculate large rectangle area

Dimensions: $10$ km $\times (5+8)$ km
$10 \times 13 = 130$ km²

Step4: Calculate small rectangle area

Dimensions: $(5+2)$ km $\times 4$ km
$7 \times 4 = 28$ km²

Step5: Sum all areas

Add the three calculated areas
$78.54 + 130 + 28$

Answer:

236.54 square kilometers