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ABCD is a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If E and F are respectively the mid points of AD and BC prove that .area (ABFE )=9/11 area (EFCD)?
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ABCD is a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If...
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ABCD is a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If...
Given Information:
ABCD is a trapezium where AB is parallel to DC. AB = 16 cm and DC = 24 cm. E and F are the midpoints of AD and BC, respectively.
To Prove:
Area of quadrilateral ABFE = 9/11 * Area of quadrilateral EFCD
Proof:
Step 1: Find the Area of Trapezium ABCD
Area of a trapezium = 1/2 * (sum of parallel sides) * height
Area of trapezium ABCD = 1/2 * (AB + DC) * height
Area of trapezium ABCD = 1/2 * (16 + 24) * height
Area of trapezium ABCD = 20 * height
Step 2: Find the Area of Triangle AEF
Since E is the midpoint of AD, AE = ED = 1/2 * AD
Since F is the midpoint of BC, BF = FC = 1/2 * BC
Therefore, triangle AEF is similar to triangle BCF with a scale factor of 1/2
Step 3: Calculate the Area of Quadrilateral ABFE
Area of quadrilateral ABFE = Area of trapezium ABCD - 2 * Area of triangle AEF
Area of quadrilateral ABFE = 20 * height - 2 * (1/4 * Area of trapezium ABCD)
Area of quadrilateral ABFE = 20 * height - 1/2 * Area of trapezium ABCD
Step 4: Find the Area of Trapezium EFCD
Since E and F are midpoints, EF is parallel to DC and EF = 1/2 * DC
Area of trapezium EFCD = 1/2 * (EF + DC) * height
Area of trapezium EFCD = 1/2 * (1/2 * 24 + 24) * height
Area of trapezium EFCD = 11 * height
Step 5: Prove the Given Statement
Area of quadrilateral ABFE = 20 * height - 1/2 * Area of trapezium ABCD
Area of quadrilateral ABFE = 20 * height - 1/2 * (20 * height)
Area of quadrilateral ABFE = 10 * height
Area of quadrilateral EFCD = 11 * height
Therefore, Area of quadrilateral ABFE = 9/11 * Area of quadrilateral EFCD, as required.
Thus, the statement is proved.
ABCD is a trapezium where AB is parallel to DC. AB = 16 cm and DC = 24 cm. E and F are the midpoints of AD and BC, respectively.
To Prove:
Area of quadrilateral ABFE = 9/11 * Area of quadrilateral EFCD
Proof:
Step 1: Find the Area of Trapezium ABCD
Area of a trapezium = 1/2 * (sum of parallel sides) * height
Area of trapezium ABCD = 1/2 * (AB + DC) * height
Area of trapezium ABCD = 1/2 * (16 + 24) * height
Area of trapezium ABCD = 20 * height
Step 2: Find the Area of Triangle AEF
Since E is the midpoint of AD, AE = ED = 1/2 * AD
Since F is the midpoint of BC, BF = FC = 1/2 * BC
Therefore, triangle AEF is similar to triangle BCF with a scale factor of 1/2
Step 3: Calculate the Area of Quadrilateral ABFE
Area of quadrilateral ABFE = Area of trapezium ABCD - 2 * Area of triangle AEF
Area of quadrilateral ABFE = 20 * height - 2 * (1/4 * Area of trapezium ABCD)
Area of quadrilateral ABFE = 20 * height - 1/2 * Area of trapezium ABCD
Step 4: Find the Area of Trapezium EFCD
Since E and F are midpoints, EF is parallel to DC and EF = 1/2 * DC
Area of trapezium EFCD = 1/2 * (EF + DC) * height
Area of trapezium EFCD = 1/2 * (1/2 * 24 + 24) * height
Area of trapezium EFCD = 11 * height
Step 5: Prove the Given Statement
Area of quadrilateral ABFE = 20 * height - 1/2 * Area of trapezium ABCD
Area of quadrilateral ABFE = 20 * height - 1/2 * (20 * height)
Area of quadrilateral ABFE = 10 * height
Area of quadrilateral EFCD = 11 * height
Therefore, Area of quadrilateral ABFE = 9/11 * Area of quadrilateral EFCD, as required.
Thus, the statement is proved.
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ABCD is a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If E and F are respectively the mid points of AD and BC prove that .area (ABFE )=9/11 area (EFCD)?
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ABCD is a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If E and F are respectively the mid points of AD and BC prove that .area (ABFE )=9/11 area (EFCD)? 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 a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If E and F are respectively the mid points of AD and BC prove that .area (ABFE )=9/11 area (EFCD)? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If E and F are respectively the mid points of AD and BC prove that .area (ABFE )=9/11 area (EFCD)?.
ABCD is a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If E and F are respectively the mid points of AD and BC prove that .area (ABFE )=9/11 area (EFCD)? 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 a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If E and F are respectively the mid points of AD and BC prove that .area (ABFE )=9/11 area (EFCD)? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a trapezium in which AB parallel DC .AB=16cm and DC =24 m ? If E and F are respectively the mid points of AD and BC prove that .area (ABFE )=9/11 area (EFCD)?.
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