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from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7
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from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD...
1-A cardboard is of the shape of a trapezium ABCD in which AB//CD, <B=900 , AB=BC=3.5cm and DC=5.5cm. A quarter circle of largest size and with centre C is removed from the cardboard. Find the area of the remaining pieced of cardboard.
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from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD...
Understanding the Shape
To calculate the area of the remaining cardboard after removing a quarter circle, we first need to analyze the trapezium ABCD.
- Dimensions:
- AB = BC = 3.5 cm
- DE (height of the trapezium from AB to CD) = 2 cm
- Angle BCD = 90 degrees
Calculating the Area of Trapezium ABCD
The area of a trapezium can be calculated using the formula:
- Area = (1/2) * (Base1 + Base2) * Height
In our case, AB and CD are the two bases, while DE is the height.
- Base 1 (AB) = 3.5 cm
- Base 2 (CD) = DE = 2 cm
- Height (DE) = 3.5 cm (since AB and BC are equal)
Now, substituting these values into the formula:
- Area = (1/2) * (3.5 + 2) * 3.5 = (1/2) * 5.5 * 3.5 = 9.625 cm²
Calculating the Area of the Quarter Circle
The radius of the quarter circle is equal to the height DE which is 2 cm. The area of a full circle is given by the formula:
- Area = π * r²
For a quarter circle, the area will be:
- Area = (1/4) * π * r²
Substituting r = 2 cm and π = 22/7:
- Area = (1/4) * (22/7) * (2)² = (1/4) * (22/7) * 4 = 22/7 cm² ≈ 3.14 cm²
Remaining Area Calculation
Now, subtract the area of the quarter circle from the area of the trapezium:
- Remaining Area = Area of Trapezium - Area of Quarter Circle
- Remaining Area = 9.625 cm² - 3.14 cm² = 6.485 cm²
Conclusion
The area of the remaining piece of cardboard is approximately 6.485 cm².
To calculate the area of the remaining cardboard after removing a quarter circle, we first need to analyze the trapezium ABCD.
- Dimensions:
- AB = BC = 3.5 cm
- DE (height of the trapezium from AB to CD) = 2 cm
- Angle BCD = 90 degrees
Calculating the Area of Trapezium ABCD
The area of a trapezium can be calculated using the formula:
- Area = (1/2) * (Base1 + Base2) * Height
In our case, AB and CD are the two bases, while DE is the height.
- Base 1 (AB) = 3.5 cm
- Base 2 (CD) = DE = 2 cm
- Height (DE) = 3.5 cm (since AB and BC are equal)
Now, substituting these values into the formula:
- Area = (1/2) * (3.5 + 2) * 3.5 = (1/2) * 5.5 * 3.5 = 9.625 cm²
Calculating the Area of the Quarter Circle
The radius of the quarter circle is equal to the height DE which is 2 cm. The area of a full circle is given by the formula:
- Area = π * r²
For a quarter circle, the area will be:
- Area = (1/4) * π * r²
Substituting r = 2 cm and π = 22/7:
- Area = (1/4) * (22/7) * (2)² = (1/4) * (22/7) * 4 = 22/7 cm² ≈ 3.14 cm²
Remaining Area Calculation
Now, subtract the area of the quarter circle from the area of the trapezium:
- Remaining Area = Area of Trapezium - Area of Quarter Circle
- Remaining Area = 9.625 cm² - 3.14 cm² = 6.485 cm²
Conclusion
The area of the remaining piece of cardboard is approximately 6.485 cm².
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from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7
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from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7 for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7 covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7.
from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7 for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7 covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7.
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from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7, a detailed solution for from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7 has been provided alongside types of from a piece of cardboard, in the shape of a trapezium ABCD, and AB CD and angle BCD =90degrees quarter circle is removed. given AB = BC =3.5CM and DE =2 cm. calculate the area of the remaining piece of the cardboard. Take pie to be 22 by 7 theory, EduRev gives you an
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