ACS Primary 2010 SA1 Math Paper 2 Q17

The shaded figure below is formed by semicircles, quarter circles and straight lines of 15 cm each. For each of the following, use the calculator value of to find
a) the perimeter of the shaded figure, correct to 2 decimal places.
b) the area of the shaded figure, correct to 2 decimal places.

Solution

(a)
Circumference of 2 semicircles (1 circle)
--> 2r
= 2 x 7.5cm
= 47.12 cm

Circumference of 2 quarter circles (1 semi circle)
-->()2r
= ()(2)() x 15cm
= 47.12 cm

Length of vertical line on the left side of figure
--> 2 x 15cm = 30cm


Perimeter of shaded figure
--> 47.12cm + 47.12cm + 30cm
= 124.25cm

Answer: 124.25 cm


(b)
Area of 2 quarter circles (1 semi circle)
-->()
= () x 15cm x 15cm
= 353.43


Area of 2 semi circles (1 circle)
-->
= x 7.5cm x 7.5 cm
= 176.71

Area of whole figure
--> 30cm x 30cm
= 900

Shaded area
--> 900 - 353.43 - 176.71
= 369.86

Answer: 369.86

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