Question

in the given figure ABCD is a parallelogram and BF perpendicular AD. point E lies on CD.If area of triangle EAB equal ro 208 sq.cm and AD equal to 20cm. find BF.​

Answer 1

The Length Of BF Is 20.8 Cm

GIVEN

ABCD is a parallelogram.

BF | AD

Area of ∆ EAB = 208 sq. cm

AD = 20 cm

TO FIND

Length of BF

SOLUTION

We can solve the above problem as follows.

According to the question-

Fig ABCD is a parallelogram

So, AD = BC = 20 cm (opposite sides of a parallelogram are equal)

Area of ∆EAB = 208 sq. cm

We know that,

If a parallelogram and triangle have a common base and altitude, the area of the triangle is equal to half of the area of the parallelogram.

So,

area of ∆EAB = area of parallelogram ABCD/2

Or,

Area of parallelogram = 2 × 208 = 416 sq. cm

Now,

Area parallelogram = Base × height.

Where,

Base = AD = 20cm

Area = 416sq.cm

Height = BF =?

Putting the values in the above formula we get,

20 × BF = 416

BF = 416/20 = 20.8

Hence, the length of BF is 20.8 cm

Refer picture for reference.

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