The figure below is made up of 2 identical quadrants of radius 7 cm that overlapped each other. The shaded square has sides of 3 cm. What is the area of the whole figure? (Take π=227\pi = \frac{22}{7})

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Worked solution

13

1. Calculate the area of one quadrant.

Area of one quadrant = 14×π×r2\frac{1}{4} \times \pi \times r^2
=14×227×7×7= \frac{1}{4} \times \frac{22}{7} \times 7 \times 7
=14×154= \frac{1}{4} \times 154
=38.5 cm2= 38.5\text{ cm}^2

2. Calculate the area of the overlapping square.

Area of square = 3×3=9 cm23 \times 3 = 9\text{ cm}^2

3. Calculate the area of the whole figure.

Area of whole figure = Area of 2 quadrants - Area of overlapping square
=2×38.5−9= 2 \times 38.5 - 9
=77−9= 77 - 9
=68 cm2= 68\text{ cm}^2

Answer

68 cm268\text{ cm}^2 (option 2)

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