Question

A trapezium such that AB II CD AD = BC = 10cm. of the perimeter of ABCD is 64 cm then find the length of CD and area of trapezium ABCD.
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Answer 1

Answer:

Given : ABCD is a trapezium, such that AB=CD and AD||BC. AD = 5 cm, BC = 9 cm and Area of trapezium = A = 35 cm², CD=?

Draw a perpendicular AE to BC from A and DF to BC from D.

Area of trapezium = A = 1/2(AD+BC)×AE = 35 cm²

Or, 1/2(5+9)×AE = 35

Or, 14×AE = 35×2

Or, AE = 35×2/14

Or, AE = 5 cm

AE=DF

AB=CD and AE & DF are perpendiculars on BC.

BE= FC=(9-5)/2=4/2=2 cm

Now, In triangle AEB, By Pythagoras Theorem

AB²=AE²+BE²=5²+2²=25+4=29

AB=√29 cm

AB=CD=√29 cm=5.385 cm

Therefore, CD = 5.385 cm