Let ABCD be a trapezium in which AB || CD and AB = 3CD. Let E be the midpoint of the diagonal BD. If [ABCD] = n[CD], what is the value of n? (Here [ denotes the area of the geometrical figure .)
Answers
Given : ABCD trapezium AB || CD . AB = 3CD
E be the midpoint of the diagonal BD
area (ABCD) = n Area ( CDE)
To Find : Value of n
Solution:
Draw BF ⊥ CD
Area of trapezium ABCD = (1/2)(AB + CD) * BF
=> Area of trapezium ABCD =(1/2)(3CD + CD) * BF
=> Area of trapezium ABCD =2CD * BF
Area of ΔBCD
= (1/2) * CD * BF
E is the mid point hence CE is median of ΔBCD
Median divides triangle in two equal area triangles
=> Area of ΔCDE = (1/2) Area of ΔBCD
=> Area of ΔCDE = (1/2) (1/2) * CD * BF
=> Area of ΔCDE = (1/4) * CD * BF
=> Area of ΔCDE = (1/8) * 2CD * BF
=> Area of ΔCDE = (1/8) * Area of trapezium ABCD
=> 8 Area of ΔCDE = Area of trapezium ABCD
=> Area of trapezium ABCD = 8 Area of ΔCDE
Hence n = 8
Value of n = 8
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Answer:
8
Step-by-step explanation:
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