Mathematics
In the figure (i) given below, calculate the area of the shaded region correct to two decimal places. (Take π = 3.142)
Mensuration
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Answer
From figure,
O is the center. In right angle triangle ABC,
Using pythagoras theorem,
⇒ AC2 = AB2 + BC2
⇒ AC2 = 52 + 122
⇒ AC2 = 25 + 144 = 169
⇒ AC = = 13 cm.
From figure,
AC is the diameter and OA is the radius = = 6.5 cm.
Area of circle = πr2
= 3.142 × (6.5)2
= 3.142 × 42.25
= 132.75 cm2.
Area of rectangle = l × b
= 12 × 5 = 60 cm2.
Area of shaded region = Area of circle - Area of rectangle
= 132.75 - 60
= 72.75 cm2.
Hence, area of shaded region = 72.75 cm2.
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