The figure is made up of 2 identical quarter circles in a rectangle.
Find the perimeter of the shaded part. (Take π=3.14\pi = 3.14)

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Worked solution

12

1. Find the length of the top side of the rectangle

The radius of each quarter circle is 1010 cm. The top side of the rectangle is equal to the sum of the two horizontal radii at the bottom.
Length of top side =10+10=20= 10 + 10 = 20 cm

2. Find the total length of the curved arcs

The two identical quarter circles make up a semicircle. The length of the curved arcs is the circumference of a semicircle with radius 1010 cm.
Length of arcs =12×2×π×r=3.14×10=31.4= \frac{1}{2} \times 2 \times \pi \times r = 3.14 \times 10 = 31.4 cm

3. Calculate the total perimeter of the shaded part

Total perimeter =20+31.4=51.4= 20 + 31.4 = 51.4 cm

Answer

51.451.4 cm (option 3)

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