Question

A field is inthe form of parallelogram hassides 60m and 40m and one of its diagonal is 80m find the area of the parallelo

Answer 1

Answer = 2323.79 cm²

Check the attachment!

Answer 2

*Refer the attachment for figure

Given: Sides of parallelogram 60 m & 40 m and diagonal 80 m.

Find: Area of parallelogram

Solution:

In ∆ABD

→ s = $\dfrac{a\:+\:b\:+\:c}{2}$

Here,

Let a = 40, b = 60, c = 80

→ s = $\dfrac{40\:+\:60\:+\:80}{2}$

→ s = $\dfrac{180}{2}$

→ s = 90

Now..

Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

→ $\sqrt{90(90 - 40)(90 - 60)(90 - 80)}$

→ $\sqrt{90(50)(30)(10)}$

→ $\sqrt{1000(9)(5)(3)(1)}$

→ 100 $\sqrt{(9)(5)(3)(1)}$

→ 100 $\sqrt{(3)(3)(5)(3)(1)}$

→ 100 (3) $\sqrt{(5)(3)(1)}$

→ 300 $\sqrt{15}$

Similarly;

In ∆BCD, we get the same result

i.e.

→ 300 $\sqrt{15}$

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Now..

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

→ 300 $\sqrt{15}$ + 300 $\sqrt{15}$

→ $\sqrt{15}$ (300 + 300)

→ $\sqrt{15}$ (600)

→ 600$\sqrt{15}$ cm²

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600$\sqrt{15}$ cm² is the area of parallelogram.

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