Question

Find the shaded area

Answer 1

Answer:

88.85 Sq m

Step-by-step explanation:

For rectangle:

Length = 18 - 7.8 = 10.2 m

Width = 7.8 m

For both semicircular arcs:

Radius (r) = 7.8/2 = 3.9 m

Area of the shaded region = Area of rectangle + 2*Area of a semicircle - Area of circle with radius 3.5 m

$= lb + 2 \times \frac{1}{2} \pi \times {(3.9)}^{2} - \pi \times {(3.5)}^{2} \\ \\ = 10.2 \times 7.8 + \pi \{{(3.9)}^{2} - (3.5)^{2} \} \\ \\ = 79.56 + \pi {(3.9 + 3.5)} (3.9 - 3.5) \\ \\ = 79.56 + 3.14 \times 7.4 \times 0.4 \\ \\ = 79.56 + 9.2944 \\ \\ = 88.8544 \\ \\ \approx 88.85 \: {m}^{2}$