Question

what is the area of this figure?
if necessary, round your answer to the nearest hundredth.
(the figure has the following side lengths: 5 km, 2 km, 4 km, 3 km, 3 km, 3 km, 2 km, 6 km)

Explanation:

Step1: Split figure into shapes

Break the figure into a rectangle, a smaller rectangle, and a semicircle.

Step2: Calculate large rectangle area

Find area of the main rectangular part.
Dimensions: length $=5+4=9$ km, width $=6-3=3$ km
Area: $9 \times 3 = 27$ km²

Step3: Calculate small rectangle area

Find area of the bottom rectangular extension.
Dimensions: length $=3$ km, width $=3$ km
Area: $3 \times 3 = 9$ km²

Step4: Calculate semicircle area

Find area of the curved semicircular part.
Radius $r=4$ km, semicircle area formula: $\frac{1}{2} \pi r^2$
Area: $\frac{1}{2} \times \pi \times 4^2 = 8\pi \approx 25.13$ km²

Step5: Sum all areas

Add the areas of the three parts together.
Total Area: $27 + 9 + 25.13 = 61.13$ km²

Answer:

$61.13$ km²