Road to PSLE: 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 $\pi$ 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)
--> 2 $\pi$ r
= 2 $\pi$ x 7.5cm
= 47.12 cm

Circumference of 2 quarter circles (1 semi circle)
-->( $\frac{1}{2}$ )2 $\pi$ r
= ( $\frac{1}{2}$ )(2)( $\pi$ ) 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)
-->( $\frac{1}{2}$ ) $\pi$ $r^{2}$
= ( $\frac{1}{2}$ ) $\pi$ x 15cm x 15cm
= 353.43 $cm^{2}$

Area of 2 semi circles (1 circle)
--> $\pi$ $r^{2}$
= $\pi$ x 7.5cm x 7.5 cm
= 176.71 $cm^{2}$

Area of whole figure
--> 30cm x 30cm
= 900 $cm^{2}$

Shaded area
--> 900 $cm^{2}$ - 353.43 $cm^{2}$ - 176.71 $cm^{2}$
= 369.86 $cm^{2}$

Answer: 369.86 $cm^{2}$

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Tuesday, May 03, 2011

ACS Primary 2010 SA1 Math Paper 2 Q17

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