Question

If the sides of the triangle are 10 cm 12 cm and 14 centimetre. find the area of the triangle​

Answer 1

Given :

The sides of the triangle are 10 cm 12 cm and 14 cm.

Find :

• Area of triangle

Formula used :

Semi perimeter ( s )= sum. of all sides of triangle /2

s = a + b + c /2

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

Solution :

Let ,

a = 10cm , b = 12cm and c = 14cm

semi - perimeter ( s ) = a + b + c /2

= 10 cm + 12 cm + 14 cm /2

= 36 cm /2

= 18 cm

Semi - perimeter ( s ) is 18 cm

$Area \: of \: triangle \\ \\ = \sqrt{s \: (s - a)(s - b)(s - c)} \\ \\ = \sqrt{18(18 - 10)(10 - 12)(18 - 14)} \\ \\ = \sqrt{18 \times 8 \times6 \times 4 } \\ \\ = \sqrt{3 \times 3 \times 2 \times 2 \times 2 \times 2 \times3 \times 2 \times 2 \times 2 } \\ \\ = 3 \times 2 \times 2 \times 2 \sqrt{3 \times 2} \\ \\ \implies 24 \sqrt{6} \: cm {}^{2}$

Hence, the area of triangle is 24 √6 cm ².