Question

Find the area of parallelogram..​

Answer 1

Step-by-step explanation:

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Please refer to the attachment for the figure

Given,

BD = 5 cm

AB = CD = 4 cm

AD = BC = 3 cm

AE = 2 cm

To find,

Area of the parallelogram ABCD

Solution,

In this parallelogram ABCD, BD is the diagonal of the parallelogram of length 5 cm

In ∆ABD and ∆BCD,

AB = CD = 4 cm

AD = BC = 3 cm

BD = BD = 5 cm ( Common side )

Therefore,

By SSS,

∆ABD is congruent to ∆BCD

As ∆ABD is congruent to ∆BCD,

Therefore,

Area of ∆ABD = Area of ∆BCD = k

Therefore,

Area of parallelogram = Area of ∆ABD + Area of ∆BCD = k + k = 2k

In ∆ ABD,

AE is acting as the altitude of the triangle

We know that,

Area of triangle = (Base x Altitude)/2

Therefore,

Area of ∆ABD = ( 5 x 2)/2 = 10/2 = 5 cm²

Area of ∆BCD = Area of ∆ABD = 5 cm²

Therefore,

Area of parallelogram = 5 + 5 = 10 cm²

Answer 2

Step-by-step explanation:

Given,

BD = 5 cm

AB = CD = 4 cm

AD = BC = 3 cm

AE = 2 cm

To find,

Area of the parallelogram ABCD

Solution,

In this parallelogram ABCD, BD is the diagonal of the parallelogram of length 5 cm

In ∆ABD and ∆BCD,

AB = CD = 4 cm

AD = BC = 3 cm

BD = BD = 5 cm ( Common side )

Therefore,

By SSS,

∆ABD is congruent to ∆BCD

As ∆ABD is congruent to ∆BCD,

Therefore,

Area of ∆ABD = Area of ∆BCD = k

Therefore,

Area of parallelogram = Area of ∆ABD + Area of ∆BCD = k + k = 2k

In ∆ ABD,

AE is acting as the altitude of the triangle

We know that,

Area of triangle = (Base x Altitude)/2

Therefore,

Area of ∆ABD = ( 5 x 2)/2 = 10/2 = 5 cm²

Area of ∆BCD = Area of ∆ABD = 5 cm²

Therefore,

Area of parallelogram = 5 + 5 = 10 cm²