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 3 shape components

The figure is made of 2 rectangles and a semicircle.

Step2: Calculate area of top rectangle

Top rectangle: length $6+4=10$ mm, width 2 mm.
Area: $10 \times 2 = 20$ mm²

Step3: Calculate area of bottom rectangle

Bottom rectangle: length 7 mm, width 4 mm.
Area: $7 \times 4 = 28$ mm²

Step4: Calculate area of semicircle

Semicircle radius $r=6$ mm. Area formula: $\frac{1}{2} \pi r^2$
$$\frac{1}{2} \times \pi \times 6^2 = 18\pi \approx 56.5487$$ mm²

Step5: Sum all component areas

Total area = $20 + 28 + 56.5487$

Answer:

104.55 mm²