Question

Three sides of a triangle is 6cm, 8cm and 10cm. It’s area (in m² ) is? (write with solution)

Answer 1

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Answer 2

Given:

The three sides of the triangle are 6 cm, 8 cm, and 10 cm.

To find:

The area of the triangle in m²

So,

When sides are given, we can use 'Heron's formula' to find the area of the triangle

Heron's formula

$= \red{\sf{\sqrt{S(S-a)(S-b)(S-c)}\ units^{2}}}$

[Here 'S' is the half of the perimeter, and a, b, c are sides of the triangles]

From the given,

The sides of the triangle are a = 6cm b = 8cm, and c = 10cm

Now,

Finding S

= (a+b+c) ÷ 2

= (6+8+10) ÷ 2

= 24 ÷ 2

= 12

And,

The area of the triangle

$= \red{\sf{\sqrt{S(S-a)(S-b)(S-c)}\ units^{2}}}$

$=\sqrt{12(12-6)(12-8)(12-10)}$

$=\sqrt{12(6)(4)(2)}$

$=\sqrt{\underline{2\times 2} \times \underline{3 \times3} \times \underline{2\times 2} \times \underline{2 \times 2}}$

= 2 × 3 × 2 × 2

= 24 cm²

Now,

We got the area of the triangle in cm².

We have to find it in m²

So,

Area = 24 ÷ 10000

= 0.0024 m²

---

As

1 m = 100 cm

$1cm = \frac{1}{100}m$

1m² = 10000 cm²

$1cm^{2} = \frac{1}{10000}m^{2}$

Hence,

The area of the triangle in m² is 0.0024 m²