Question

Find area of parellogram whose adjacent side are 130&140 & one diagonal is 150 m

Answer 1

Question : -

Find the area of a parallelogram whose adjacent sides are 130 m and 140 m respectively and one of it's diagonal is 150 m.

Answer : -

Given that,

Adjacent side 1 = 130 m

Adjacent side 2 = 140 m

Diagonal 1 = 150 m

To find,

The area of ||logram = ?

Assumption,

Let AB = 130 m

Let BC = 140 m

Let AC = 150 m

As we know,

"The diagonal of a parallelogram divides it into two congruent triangles."

"Opposite side of a parallelogram are equal."

In the above figure,

△ABC ≅ △ADC

Therefore,

AD = BC = 140 m

DC = AB = 130 m

As we don't have it's height,

We have to find the area of △ABC and area of △ADC and then add them together.

Area of △ABC,

By using Heron's formula,

$\sqrt{s(s - a)(s - b)(s - c)}$

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

Here, a = AB = 130 m

b = BC = 140 m

c = AC = 150 m

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

s = $\frac{(130+140+150)m}{2}$

s = $\frac{420\:m}{2}$

s = 210 m

[By substituting the value of s in the above formula],

$\sqrt{s(s - a)(s - b)(s - c)}$

Area =

$\sqrt{210(210 - 130)(210 - 140)(210 - 150)}$

Area =

$\sqrt{210(80)(70)(60)}$

Area =

$\sqrt{(2 \times 3 \times5 \times 7)(2 \times 2 \times 2 \times 2 \times 5)(2 \times 5 \times 3)(2 \times 2 \times 3 \times 5) }$

Area =

$\sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 7}$

Area =

$\sqrt{8400}$

Area =

${91.65} \: {m}^{2}$

As △ABC ≅ △ADC,

There area must be same.

Therefore, area of △ADC = 91.65 m²

Ar(||logram ABCD) = ar(△ABC) + ar(△ADC)

Ar(||logram ABCD) = 91.65 m² + 91.65 m²

Ar(||logram ABCD) = 183.5 m²

Therefore, area = 183.5 m²