ABCD is a trapezium in which AB is parallel to DC. Let E and F be the midpoints on AD and BC respectively. If EF=10cm and ABDC=4cm, then what is the value of AB×DC ?
Given: AB|EF|DC EF=10cm AB−DC=4cm Formula Used: Length of midsegment =‌
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(Sum of parallel sides ) Calculation: We have AB−DC=4cm‌‌⋯(1) In the given below, E is the mid - point of the side AD of the trapezium ABCD with AB parallel to DC . A line through E drawn to AB intersects Using the above formula, we can write EF=‌
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(AB+DC) ⇒EF=‌
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(4+DC+DC)‌‌‌ [Fomm equation ‌(1)]
⇒20=4+2DC ⇒2DC=16 ⇒DC=8cm Put this value in equation (1), ⇒AB−8=4 ⇒AB=12cm Hence, the required value ⇒AB×DC=12×8 ⇒AB×DC=96‌ square ‌cm ∴AB×DC is 96sq.cm