Question

what is the area of this figure?
6 mm
6 mm
2 mm
2 mm
7 mm
5 mm
4 mm
if necessary, round your answer to the nearest hundredth.

Explanation:

Step1: Identify shape components

The figure is made of 3 rectangles and a semicircle.

Step2: Calculate top rectangle area

Area = length × width = $6 \times 2 = 12$ mm²

Step3: Calculate middle rectangle area

First find its total height: $6 + 2 = 8$ mm, width = $4$ mm. Area = $4 \times (8 - 2) = 4 \times 6 = 24$ mm²

Step4: Calculate bottom rectangle area

Area = length × width = $4 \times 7 = 28$ mm²

Step5: Calculate semicircle area

Radius $r = \frac{6 + 2}{2} = 4$ mm. Area = $\frac{1}{2} \pi r^2 = \frac{1}{2} \times \pi \times 4^2 = 8\pi \approx 25.13$ mm²

Step6: Sum all areas

Total area = $12 + 24 + 28 + 25.13$

Answer:

89.13 mm²