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Find the area of a parallelogram ABCD in which AB = 28 cm, BC

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Find the area of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm.

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Find the area of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm.

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Text solutionVerified

Δ

ABC

Take a = 26cm, b = 30cm and c = 28cm

So we get

s = \frac{a + b + c}{2}

s = \frac{26 + 30 + 28}{2}

By division

s=42cm

We know that

Area=

s (s - a) (s - b) (s - c)

By substituting the values

Area=

42 (42 - 26) (42 - 30) (42 - 28)

So we get

Area=

42 \times 16 \times 12 \times 14

It can be written as

Area=

14 \times 3 \times 16 \times 4 \times 3 \times 14

On further calculation

Area=

14 \times 14 \times 3 \times 3 \times 16 \times 4

So we get

Area=

14 \times 3 \times 4 \times 2

By multiplication

Area=

336 c m^{2}

We know that the diagonal divides the parallelogram into two equal area

So the area of parallelogram ABCD=Area of

Δ

ABC+Area of

Δ

ACD

It can be written as

Area of parallelogram ABCD=2(Area of

Δ

ABC)

By substituting the values

Area of parallelogram ABCD=2(336)

By multiplication

Area of parallelogram ABCD=

672 c m^{2}

Therefore, the area of parallelogram ABCD is

672 c m^{2}

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Question Text	Find the area of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm.
Answer Type	Text solution:1
Upvotes	154

Find the area of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm.

Text solutionVerified

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