Question

Find the area of a triangle whose equal sides are 13 cm,14 cm and 15 cm using Hero's formula

Answer 1

84 cm²

Step-by-step explanation:

QUESTION :-

Find the area of a triangle whose sides are 13 cm, 14 cm and 15 cm. Using Hero's formula.

________________________

SOLUTION :-

We have sides,

• a = 13 cm
• b = 14 cm
• c = 15 cm

Have to find,

s (semi-perimeter)

s = (a+b+c)/2

=> (13+14+15)/2 cm

=> 42/2 cm

=> 21 cm

Now,

area of triangle using Hero's formula -

$= > \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = > \sqrt{21(21 - 13)(21 - 14)(21 - 15)} {cm}^{2} \\ \\ = > \sqrt{21 \times 8 \times 7 \times 6} {cm}^{2} \\ \\ = > \sqrt{7 \times 3 \times 2 \times 2\times2 \times 7 \times 2 \times 3 } {cm}^{2} \\ \\ = > \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7 \times 7} {cm}^{2} \\ \\ = > \sqrt{ {2}^{2} \times {2}^{2} \times { 3 }^{2} \times {7}^{2} } {cm}^{2} \\ \\ = > 2 \times 2 \times 3 \times 7 {cm}^{2} \\ \\ = > 84 {cm}^{2}$

So,

the area of triangle is 84 cm².

hope it helps.

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