Find the area of the shaded region in figure, where ABCD is a square of side 10 cm. and semicircles are drawn with each side of the square as diameter (use π = 3.14)
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hey here's the answer to your question...
First we'll name the four semicircles as 1,2,3 and 4.
Total area of 1 and 2:-
[10×10-π×5²/2-π×5²]
=21.45
Total area of 3 and 4
=21.45
Area of square ABCD- Area of semicircles:-
21.45+21.45=42.9
10×10-42.9
=100-42.9
=57.1
hope it helps...please mark my answer as brainliest....
First we'll name the four semicircles as 1,2,3 and 4.
Total area of 1 and 2:-
[10×10-π×5²/2-π×5²]
=21.45
Total area of 3 and 4
=21.45
Area of square ABCD- Area of semicircles:-
21.45+21.45=42.9
10×10-42.9
=100-42.9
=57.1
hope it helps...please mark my answer as brainliest....
Answered by
22
1 ) ABCD is a square of side 10 cm.
Area of the Square = side × side
= 10cm × 10 cm
= 100 cm² ----( 1 )
2 ) From figure ( ii ) ,
area of ( a + b ) region
= area of the square - 2 × area of semicircle
= 100 - 2 × ( πr²)/2
= 100 - πr²
= 100 - 3.14 × 5²
= 100 - 88.5
= 11.5 cm²
3 ) Similarly , from figure iii )
area of ( b + d ) region = 11.5 cm²
4 ) Area of required shaded region
= area of the square - ( a+b+c+d) area
= 100 - ( 11.5 + 11.5 )
= 100 - 23
= 77 cm²
*****
Area of the Square = side × side
= 10cm × 10 cm
= 100 cm² ----( 1 )
2 ) From figure ( ii ) ,
area of ( a + b ) region
= area of the square - 2 × area of semicircle
= 100 - 2 × ( πr²)/2
= 100 - πr²
= 100 - 3.14 × 5²
= 100 - 88.5
= 11.5 cm²
3 ) Similarly , from figure iii )
area of ( b + d ) region = 11.5 cm²
4 ) Area of required shaded region
= area of the square - ( a+b+c+d) area
= 100 - ( 11.5 + 11.5 )
= 100 - 23
= 77 cm²
*****
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