In a square abcd of side 10cm and semicircle are drawn with each side of the square as diameter. Find are of the shaded portion of the square
Answers
Let Unshaded regions be I, II, III and IV
Area of I + Area of III= Area of ABCD – Areas of two semicircles
= ( 10X10 - 2X1/2 X 3.14 X 5 X5)
= (100 - 3.14 * 25)
=21.5 cm²
similarly Area of II and IV is equal to 21.5cm²
So,
Area of shaded region = 100 - (21.5 + 21.5)
= 57cm²
Answer:
Let Unshaded regions be 1, 2, 3 and 4
Area of 1 + Area of 3= Area of ABCD – Areas of two semicircles of each of radius 5 cm
Area of 1 and 3 = ( 10 * 10 - 2 * 1/2 * 3.14 * 5 *5) [Area of semi circle = 1/2 pie r²]
= (100 - 3.14 * 25)
= (100 - 78.5)
=21.5 cm²
So,
Even the Area of 2 and 4 is equal to 21.5cm²
So,
Area of shaded region = Area of ABCD - Area 0f( 1+2+3+4)
= 100 - (21.5 + 21.5)
= 100 - 43
Area of shaded region = 57cm²
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