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If ABCD is trapezium withAB//DC and angleBCD=30' IF BGEC is a sector of a cirlce with centreC and AB= 7 cm , DE= 4 cm and BF = 3.5 cm .find the area of a shaded region( pie r =22 by 7)
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If ABCD is trapezium withAB//DC and angleBCD=30' IF BGEC is a sector o...
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If ABCD is trapezium withAB//DC and angleBCD=30' IF BGEC is a sector o...
Given data:
- Trapezium ABCD with AB//DC and angle BCD = 30'
- BGEC is a sector of a circle with center C
- AB = 7 cm, DE = 4 cm, BF = 3.5 cm
- πr = 22/7
Finding the Area of Shaded Region:
1. Finding the Length of BC:
Since AB//DC, we can consider triangle BCD as a right-angled triangle.
Using trigonometry, we can find BC:
tan(30') = BC/AB
tan(30') = BC/7
BC = 7 * tan(30')
BC ≈ 7 * 0.5774
BC ≈ 4.04 cm
2. Finding the Radius of the Circle:
Since BGEC is a sector of a circle with center C, BGEC is a quadrant of the circle.
The radius of the circle will be BC + BF = 4.04 + 3.5 = 7.54 cm
r = 7.54 cm
3. Finding the Area of the Shaded Region:
Area of the sector = (θ/360) * πr^2
θ = 30' (angle BCD)
Area of the sector = (30/360) * (22/7) * (7.54)^2
Area of the sector ≈ 14.98 cm^2
Area of triangle BCD = (1/2) * BC * DE
Area of triangle BCD = (1/2) * 4.04 * 4
Area of triangle BCD ≈ 8.08 cm^2
Area of the shaded region = Area of the sector - Area of triangle BCD
Area of the shaded region ≈ 14.98 - 8.08
Area of the shaded region ≈ 6.90 cm^2
Therefore, the area of the shaded region is approximately 6.90 cm^2.
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If ABCD is trapezium withAB//DC and angleBCD=30' IF BGEC is a sector of a cirlce with centreC and AB= 7 cm , DE= 4 cm and BF = 3.5 cm .find the area of a shaded region( pie r =22 by 7)
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If ABCD is trapezium withAB//DC and angleBCD=30' IF BGEC is a sector of a cirlce with centreC and AB= 7 cm , DE= 4 cm and BF = 3.5 cm .find the area of a shaded region( pie r =22 by 7) for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If ABCD is trapezium withAB//DC and angleBCD=30' IF BGEC is a sector of a cirlce with centreC and AB= 7 cm , DE= 4 cm and BF = 3.5 cm .find the area of a shaded region( pie r =22 by 7) covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ABCD is trapezium withAB//DC and angleBCD=30' IF BGEC is a sector of a cirlce with centreC and AB= 7 cm , DE= 4 cm and BF = 3.5 cm .find the area of a shaded region( pie r =22 by 7).
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