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ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are the midpoint of non parellel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is?
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ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are...
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ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are...
Understanding the Trapezium ABCD
ABCD is a trapezium with parallel sides AB and DC. Let’s denote the lengths of these sides as follows:
- AB = a
- DC = b
In this trapezium, E and T are the midpoints of the non-parallel sides AD and BC, respectively.
Finding the Areas of Quadrilaterals
To find the ratio of the areas of quadrilaterals ABFE and EFCD, we first need to understand how the areas relate to the lengths of the parallel sides and the height of the trapezium.
Area of Quadrilateral ABFE
1. The area of trapezium ABCD can be expressed as:
- Area = (1/2) * (AB + DC) * height
- Area = (1/2) * (a + b) * h
2. The quadrilateral ABFE consists of the trapezium formed by AB and EF, where EF is the line segment joining midpoints E and T. The length of EF will be:
- EF = (AB + DC) / 2 = (a + b) / 2
3. Hence, the area of quadrilateral ABFE can be calculated using:
- Area ABFE = (1/2) * (AB + EF) * (h/2)
- Area ABFE = (1/2) * (a + (a + b)/2) * (h/2)
Area of Quadrilateral EFCD
1. Similarly, for quadrilateral EFCD:
- Area EFCD = (1/2) * (EF + DC) * (h/2)
- Area EFCD = (1/2) * ((a + b)/2 + b) * (h/2)
Calculating the Ratio of Areas
Now, to find the ratio of the areas of quadrilaterals ABFE and EFCD:
- Ratio = Area ABFE / Area EFCD
This ratio simplifies to:
- Ratio = (a + b) / b
Thus, the final ratio of the areas of quadrilaterals ABFE and EFCD is:
Final Ratio: (a + b) : b
ABCD is a trapezium with parallel sides AB and DC. Let’s denote the lengths of these sides as follows:
- AB = a
- DC = b
In this trapezium, E and T are the midpoints of the non-parallel sides AD and BC, respectively.
Finding the Areas of Quadrilaterals
To find the ratio of the areas of quadrilaterals ABFE and EFCD, we first need to understand how the areas relate to the lengths of the parallel sides and the height of the trapezium.
Area of Quadrilateral ABFE
1. The area of trapezium ABCD can be expressed as:
- Area = (1/2) * (AB + DC) * height
- Area = (1/2) * (a + b) * h
2. The quadrilateral ABFE consists of the trapezium formed by AB and EF, where EF is the line segment joining midpoints E and T. The length of EF will be:
- EF = (AB + DC) / 2 = (a + b) / 2
3. Hence, the area of quadrilateral ABFE can be calculated using:
- Area ABFE = (1/2) * (AB + EF) * (h/2)
- Area ABFE = (1/2) * (a + (a + b)/2) * (h/2)
Area of Quadrilateral EFCD
1. Similarly, for quadrilateral EFCD:
- Area EFCD = (1/2) * (EF + DC) * (h/2)
- Area EFCD = (1/2) * ((a + b)/2 + b) * (h/2)
Calculating the Ratio of Areas
Now, to find the ratio of the areas of quadrilaterals ABFE and EFCD:
- Ratio = Area ABFE / Area EFCD
This ratio simplifies to:
- Ratio = (a + b) / b
Thus, the final ratio of the areas of quadrilaterals ABFE and EFCD is:
Final Ratio: (a + b) : b
Community Answer
ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are...
3a+b:3b+a
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ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are the midpoint of non parellel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is?
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ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are the midpoint of non parellel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are the midpoint of non parellel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are the midpoint of non parellel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is?.
ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are the midpoint of non parellel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are the midpoint of non parellel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is trapezium with parallel sides AB= a and DC= b . If E and T are the midpoint of non parellel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is?.
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