Question 11:
Diagram 6 shows a semicircle landscape garden built by Kamal at his house. The garden consists of a herbal garden and a quadrant fish pound. He plans to fence the herbal garden.
Diagram 6
POKQ is a straight line and K is the midpoint of OQ. It is given that PQ = 14 m and OP : OK = 2:1. Calculate
(a) the total length, in m, of the fence for the herbal garden, [3 marks]
(b) the area, in m2, of the herbal garden. [3 marks]
Solution:
(a)
Length of arc PQ=180o360o×2πr =180o360o×2×227×7 =22 mLength of arc LK=90o360o×2×227×3.5 =5.5 mTotal length of fence=(22+3.5+5.5+3.5+7)m =41.5 m
(b)
Total area of semicircle=12πr2 =12×227×72 =77 m2Total area of quadrant of fish pond=14πr2=14×227×3.52=9.625 m2Area of herbal garden=77 m2−9.625 m2 =67.375 m2
Diagram 6 shows a semicircle landscape garden built by Kamal at his house. The garden consists of a herbal garden and a quadrant fish pound. He plans to fence the herbal garden.

POKQ is a straight line and K is the midpoint of OQ. It is given that PQ = 14 m and OP : OK = 2:1. Calculate
(a) the total length, in m, of the fence for the herbal garden, [3 marks]
(b) the area, in m2, of the herbal garden. [3 marks]
Solution:
(a)
Length of arc PQ=180o360o×2πr =180o360o×2×227×7 =22 mLength of arc LK=90o360o×2×227×3.5 =5.5 mTotal length of fence=(22+3.5+5.5+3.5+7)m =41.5 m
(b)
Total area of semicircle=12πr2 =12×227×72 =77 m2Total area of quadrant of fish pond=14πr2=14×227×3.52=9.625 m2Area of herbal garden=77 m2−9.625 m2 =67.375 m2