In the diagram above, QR is the diameter of the semicircle QR. Find the area of the figure to the nearest whole number. [\(\pi = \frac{22}{7}\)]
Attached Figure / Diagram
A
89 cm2
B
70 cm2
C
90 cm2
D
80 cm2
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Area of rectangle PQRS = \(10 \times 7 = 70cm^2\)
Area of semi-circle: \(\frac{\pi r^{2}}{2}\)
r = \(\frac{7}{2} cm\)
Area of semi-circle = \(\frac{1}{2} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}\)
= \(\frac{77}{4} = 19.25 cm^{2}\)
Area of figure = \((70 + 19.25) cm^{2}\)
= 89.25 cm\(^{2} \approxeq\) 89 cm\(^{2}\)
Source: Myschool Past Questions Archive (Record #8833)