Question

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

Answer 1

Answer:

In △ ABC.

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

So the area of parallelogram ABCD = Area of △ ABC + Area of △ ACD.

Area of parallelogram ABCD = 2(Area of △ ABC)

Therefore, the area of parallelogram ABCD is 672 cm2.

Step-by-step explanation:

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Answer 2

Given :–

• ABCD is a parallelogram.
• AB = 28cm
• BC = 26cm
• Diagonal AC = 30cm

To Find :–

• Area of a parallelogram.

Solution :–

According to the question,

A diagonal of parallelogram divides into two equal triangles.

First, we need to find the area of a triangle.

So,

In ∆ABC,

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

Where,

⟹ $s = \frac{a + b + c}{2}$

• a = 26cm
• b = 30cm
• c = 28cm

⟹ $s = \dfrac{26 + 30 + 28}{2}$

⟹ $s = \dfrac{ \cancel{84}}{ \cancel2}$

⟹ $s = 42$

• s = 42

Now, put all the values in the area of a triangle.

⟹ $\sqrt{42(42 - 26)(42 - 30)(42 - 28)}$

⟹ $\sqrt{42(16)(12)(14)}$

⟹ $\sqrt{(14 \times 3)(4 \times 4)(3 \times 4)(14)}$

⟹ $14 \times 4 \times 3 \sqrt{4}$

⟹ $14 \times 12 \sqrt{4}$

⟹ $168 \sqrt{4}$

⟹ $168(2)$

⟹ ${336 \: cm}^{2}$

Hence,

The area of a triangle is 336cm².

Now, we have to find the area of the parallelogram.

Area of parallelogram = Area of ∆ABC + Area of ∆ACD

We can also write as,

Area of parallelogram = 2(Area of a triangle)

• Area of a triangle = 336cm²

⟹ 2(336)

⟹ 672cm²

Hence,

Area of the parallelogram is 672cm².