Question

the side of a triangle are 14 cm , 6 cm and 10 cm long.find the area of the triangle​

Answer 1

Given :-

First side = 14 cm

Second side = 6 cm

Third side = 10 cm

To Find :-

The area of the triangle.

Analysis :-

Firstly, find the semi perimeter by substituting the values given in it's respective formula.

Using Heron's formula, find the area accordingly.

Solution :-

We know that,

• s = Semi perimeter
• a = Area

By the formula,

$\underline{\boxed{\sf Semi \ perimeter=\dfrac{a+b+c}{2} }}$

Given that,

First side (a) = 14 cm

Second side (b) = 6 cm

Third side (c) = 10 cm

Substituting their values,

s = 14+6+10/2

s = 30/2

s = 15

Therefore, the semi perimeter of the triangle is 15 cm.

Using Heron's formula,

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

Given that,

Semi perimeter (s) = 15 cm

First side (a) = 14 cm

Second side (b) = 6 cm

Third side (c) = 10 cm

Substituting their values,

$\sf =\sqrt{15(15-14)(15-6)(15-10)}$

$\sf =\sqrt{15 \times 1 \times 9 \times 5}$

$\sf =\sqrt{675}$

$\sf = 25.98 \ cm^2$

Therefore, area of the triangle is 25.98 cm².

Answer 2

Answer:

15 ✓3

Step-by-step explanation:

Strategy:

Let's start by stating Heron's formula.

In a triangle with sides \goldD{a}astart color #e07d10, a, end color #e07d10, \blueD{b}bstart color #11accd, b, end color #11accd, and \redD{c}cstart color #e84d39, c, end color #e84d39,

\text{Area} =\sqrt{\maroonD{s}(\maroonD{s}-\goldD{a})(\maroonD{s}-\blueD{b})(\maroonD{s}-\redD{c})}Area=

s(s−a)(s−b)(s−c)

start text, A, r, e, a, end text, equals, square root of, start color #ca337c, s, end color #ca337c, left parenthesis, start color #ca337c, s, end color #ca337c, minus, start color #e07d10, a, end color #e07d10, right parenthesis, left parenthesis, start color #ca337c, s, end color #ca337c, minus, start color #11accd, b, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, s, end color #ca337c, minus, start color #e84d39, c, end color #e84d39, right parenthesis, end square root

Where \maroonD{s}sstart color #ca337c, s, end color #ca337c is the semi-perimeter.