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Question
In the given figure, ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =
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Solution
Given: (1) ABCD is a parallelogram.
(2) AB = 12 cm
(3) AE = 7.5 cm
(4) CF = 15cm
To find: AD
Calculation: We know that,
Area of a parallelogram = base × height
Area of a parallelogram ABCD = DC ×AE (with DC as base and AE as height) ……(1)
Area of a parallelogram ABCD = AD ×CF (with DC as base and AE as height) ……(2)
Since equation 1 and 2 both are Area of a parallelogram ABCD
`DC xx AE = AD xx CF`
`AD = (DC xx AE)/(CF)`
`AD = (AB xx AE)/(CF)` (AB = DC , opposite sides of parallelogram are eual )
`AD = (12 xx 7.5)/15`
AD = 6 cm
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