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In the given figure,ABC is a right angle...

In the given figure,ABC is a right angled triangle in which `/_A=90^@`,AB=21 cm and AC=28 cm.Semi-circles are drawn on AB, BC and AC as diameters. Find the area of shaded region.

Text Solution

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`BC^2 = AB^2 +AC^2`
`BC^2 = 21^2 + 28^2`
`21^2 = (7*3)^2= 7^2*3^2`
`28^2 = 7^2*4^2`
so, `BC^2= 7^2(3^2+4^2)`
`BC^2 = 7^2 * 5^2 `
`BC= 7*5 = 35`
for shaded region = `pi/2(21/2)^2 + pi/2(28/2)^2 + 1/2*21*28 - pi/2(35/2)^2 `
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