Question

find the area of triangle whose side is 18 cm 10 cm and whose perimeter is 42 CM​

Answer 1

$\bf\huge\underline{Answer}$

The area of the triangle is 21√11 cm²

Explanation :-

Given :

First side of the triangle (a) = 18 cm

Second side of the triangle (b) = 10 cm

Perimeter of the triangle = 42 cm

To find :

Area of the triangle

Solution :

The first and second side of the triangle are given, but the third side isn't given.

Let the third side of the triangle be c

We know that,

Perimeter = (a + b + c) cm

or, Perimeter = 42 cm

or, (18 + 10 + c) = 42 cm

or, 28 + c = 42 cm

or, c = (42 - 28) cm

or, c = 14 cm

Hence, the third side of the triangle is 14 cm.

Now,

The sides of the following triangle are 18 cm, 10 cm and 14 cm.

From the given sides, we can guess that's an scalene triangle as scalene triangles have three different sides as given.

Therefore, Semi-Perimeter => Perimeter/2 = 42/2 = 21 cm

We know that,

Area of scalene triangle :-

$= \sqrt{s(s - a)(s - b)(s - c)} sq.unit$

$= \sqrt{21(21 - 18)(21 - 10)(21 - 14)} \: {cm}^{2}$

$= \sqrt{21 \times 3 \times 11 \times 7} \: {cm}^{2}$

$= \sqrt{7 \times 3 \times 3 \times 11 \times 7} \: {cm}^{2}$

$= 7 \times 3 \sqrt{11} \: {cm}^{2}$

$= 21 \sqrt{11 } \: {cm}^{2}$

Hence, the area of the triangle is 21√11 cm².

Answer 2

Question= Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.

Solution⬇️

Given the perimeter of the triangle is

and the sides length

and

So,

Or,

So, the semi perimeter of the triangle will be:

Therefore, the area given by the Heron's Formula will be,

Hence, the area of the triangle is