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Find the Perimeter of the Shaded Region in Figure 4, If Abcd is a Square of Side 14 Cm and Apb and Cpd Are Semicircles. Use π 22 7 - Mathematics

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Sum

Find the perimeter of the shaded region in Figure 4, if ABCD is a square of side 14 cm and APB and CPD are semicircles. Use `pi = 22/7`

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Solution

The length of the sides of square ABCD is 14 cm.

∴ AB = BC = CD = AD = 14 cm

Radius of each semi-circular portion `14/2 "cm" =7 "cm"`

Perimeter of the shaded region = Perimeter of semi-circle APB + perimeter of semi-circle CPD + BC + AD

`\text{Perimeterof semi - circle APB}=1/2xx2pixxradius=1/2xx2pixx7 cm =22/7 xx7cm =22cm`

`\text{Perimeterof semi - circle CPD}=1/2xx2pixxradius=1/2xx2pixx7 cm =22/7 xx7cm =22cm`

∴ Perimeter of the shaded region = 22 cm + 22 cm + 14 cm + 14 cm = 72 cm

Concept: Areas of Combinations of Plane Figures
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