Question

in the given figure given below O is the centre of the circle with ac= 24 cm ab = 7 cm and angle b o d =90° find the area of the shaded region

Answer 1

(BC)^2=(576+49)^2 centimeter-square

BC=25centimeter

BC is diameter of the circle

OC = the radius of the circle=25/2=12.5centimeter

Area of the sector COD,(A2)

A2=theta/360 degree x pi x radius^2

A2=90 degree/360 degree * 22/7 *25/2*25/2

A2=122.77 centimeter square

Area of the circle(A3)=pi*radius^2

A3=22/7*25/2*25/2

Area of the shaded region =Area of the circle(Area of the Triangle ABC + Area of the sector COD)

Area of the shaded regions=A3(A1+A2)

Area of the shaded regions=284.30 centimeter-square.

Answer 2

angle BAC =90°
by Pythagoras theorem
BC² =AC² + AB²
=24²+7²
=576+49
BC= √ 625
BC=25cm therefore radius is 12.5cm
Area of shaded region= Area of semicircle- area of triangle+ area of sector.
=πr²/2 - 1/2 base × height + 90°/360°×πr²
=1/2[πr²-base×height] + 90/360×πr²
=1/2[ 3.14×(12.5)²]-(24×7)+1/4×3.14×(12.5)²
=322.625/2+122.65625
=161.3125+122.65625
=283.96875
=283.97cm²
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