Question

In the given figure, ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =

Answer 1

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