4 In the given fig , ABC is a Δrt d at B, with AB = - Maths - Areas Related to Circles

Question

4 In the given fig , ABC is a Δrt ∠d at B, with
AB = 14 cm & BC = 24 cm With the vertices A, B and C as
centres, arcs are drawn each of radius 7 cm
Find the area of the shaded region Use   π = 22 7

5 In fig , ABC is a right angled triangle, right angled at A
Semicircles are drawn on AB, AC & BC as diameters Find the area
of the shaded region
(Ans 6 sq units)

Neha Sethi · Accepted Answer

Dear student
4The area of shaded region=Area of △ABC-area of 3 sectors
Now area of △ABC  right angled at B=12×base×height=12×BC×AB=12×24×14   Given: AB=14 cm and BC=24 cm=168 cm2Consider △ABC,by angle sum property we have∠A+∠B+∠C=180° 
1Now we know that area of sector=θ360°×πr2 , where r is the radius of the circleArea of 3 sectors=∠A360°×πr2 +∠B360°×πr2 +∠C360°×πr2 =πr2360°∠A+∠B+∠C=1360°×72×227  ∠A+∠B+∠C       Given r=7 cm=180°360°×7×22   using 1=77 cm3So, area of shaded region=Area of △ABC-area of 3 sectors=168 cm2-77 cm2=91 cm2
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