Question

Two adjacent side of a parallelogram are 74 cm and 40 cm one of its diagonal is 102 CM area of the parallelogram is

Answer 1

$\huge{\bf{\underline{\purple{Solution :}}}}$

Given,

• Two adjacent side of Parallelogram are 74 cm and 40 cm .
• One of parallelogram diagonal is 102 cm

To Find :

• Area of Parallelogram = ?

Find :

• Suppose the two adjacent side of parallelogram be a and b side of traingle .
• Suppose the length of diagonal be c side of traingle

Therefore ,

⇒These two sides and one diagonal divide the parallelogram into two triangle .

Now Find Triangle Area :

$\implies \therefore \bold{Semi - Perimeter = \frac{a + b + c}{2}}$

$\implies \bold{ s = \frac{74 + 40 + 102 }{2}}$

$\implies \bold{ s = \frac{216}{2} = 108 \ cm }$

Now Using Heron's Formula to Find Area of  triangle :

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

$: \implies \bold{\sqrt{108(108-74)(108-40)(108-102)}}$

$: \implies \bold{\sqrt{108 \times 34 \times 68 \times 6}}$

$: \implies \bold{6 \times 2 \times 3 \times 34}$

$: \implies \bold{1224 \ cm^{2} }$

Now Find Area of Parallelogram :

⇒Area of Parallelogram = 2 x Area of Triangle

⇒2 x 1224

⇒2448 cm ²(Answer)

$\rule{200}2$

Answer 2

Step-by-step explanation:

Let us assume that the two adjacent sides of the parallelogram are a and b

So,

a = 74 cm, b = 40 cm

And,

The length of diagonal :-

c = 102 cm

These two sides and the diagonal forms a triangle

Semi perimeter

s = ( a + b + c ) / 2

s = ( 74 + 40 + 102 ) / 2 = 216 / 2 = 108 cm

Now we will apply Heron's formula,

Area of triangle

Δ = √[s (s - a) (s - b) (s - c)]

= √[108 (108 - 74) (108 - 40) (108 - 102)]

= √{108 × 34 × 68 × 6}

= √{3 × 4 × 9 × 34 × 2 × 34 × 6}

= √{3 × 4 × 9 × 34 × 2 × 34 × 6}

= √{6 × 4 × 9 × 34 × 34 × 6}

= 6 × 2 × 3 × 34

= 1224 sq cm

Now , As we know

Area of parallelogram = 2 × area of triangle

= 2 × 1224

= 2448 sq cm

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