Question

If the sides of triangle is 10cm,12cm,& 14 cm find the area of the triangle by using herons formula

Answer 1

Solutions :-


Given :

abc is a triangle.

Side a = 10 cm
Side b = 12 cm
Side c = 14 cm


Find the semi perimeter (s) of triangle :-

s = (a+b+c)/2 unit
= (10+12+14)/2 cm
= 36/2 cm = 18 cm


Find the area of triangle by using the heron's formula :-

$area = \sqrt{s(s - a)(s - b)(s - c) } \\ \\ = \sqrt{18(18 - 10)(18 - 12)(18 - 14)} \\ \\ = \sqrt{18 \times 8 \times 6 \times 4} \\ \\ = \sqrt{2 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2 \times 3 \times 2 \times 2} \\ \\ = 2 \times 2 \times 2 \times 3 \times \sqrt{2 \times 3} \\ \\ = 24 \sqrt{6}$


Hence,
Area of triangle = 24√6 cm²

Answer 2

Solutions :-

We have,

The sides of triangle is 10cm, 12cm & 14 cm.

Semi perimeter of triangle

$= \frac{10 + 12 + 14}{2} \\ \\ = \frac{36}{2} = 18 \: cm$

By Heron's formula :-

Area of triangle

$= \sqrt{18(18 - 10)(18 - 12)(18 - 14)} \\ \\ = \sqrt{18 \times 8 \times 6 \times 4} \\ \\ = \sqrt{2 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2 \times 3 \times 2 \times 2} \\ \\ = 2 \times 2 \times 2 \times 3 \times \sqrt{2 \times 3 } \\ \\ = 24 \sqrt{6}$

Answer : Area of Triangle = $24 \sqrt{6}$ cm² or 58.78 cm²