In the diagram above, QR is in the diameter of the semicircle QR. Find the area of the figure to the nearest whole number. [(pi = frac{22}{7})]
- A.
89 cm^{2} - B.
70 cm^{2} - C.
90 cm^{2} - D.
80 cm^{2}
Correct Answer: Option A
Explanation
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} = 18.75 cm^{2})
Area of figure = ((70 + 18.75) cm^{2})
= 88.75 cm(^{2} approxeq) 89 cm(^{2})