Question

is sides of a triangle are 45cm, 39 cm, 84200
find Area of triangle using Heron's formula​

Answer 1

Answer:

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Answer 2

Correct Question :

A Triangle is having sides of measurements 45cm, 39 cm, 42 cm .Find the area by using heron's formula.

$\bullet \: \:$ Answer :

Here, it is stated that the triangle is having three sides , measurement 45cm, 39 cm, 42 cm respectively. So, it has asked us to find out the area of the given triangle by using the heron's formula.

For that, we will find the semi permeter of the triangle and thereafter we will be using the formula for finding the area of the triangle.

★ Formula required :

Area of a Scalene triangle :

Semi perimeter = s = (a + b + c)/2

⠀⠀⠀⠀⠀⠀⠀⠀⠀A = √[s(s - a)(s - b)(s - c)]

Where :

• A = Area of the triangle

• a, b and c = Sides of the triangle

• s = Semi-perimeter of the triangle

Given Sides :

• Side of the triangle, a = 45 cm

• Side of the triangle, b = 39 cm

• Side of the triangle, c = 42 cm

Now, we know that the perimeter of the Triangle is the sum of its all three sides.

So,

a + b + c = Perimeter

→ 45 + 39 + 42 = 126

Let's find out the semi-perimeter of the triangle :

Semi perimeter : Half of the perimeter i.e, Perimeter/2

So,

126/2 = 63

Here,

∴ s = 63 cm

The semi-perimeter of the triangle is 63 cm.

Now using the formula for area of a triangle and substituting the values in it, we get :

==> A = √[s(s - a)(s - b)(s - c)]

==> A = √[63 × (63 - 45) × (63 - 39) × (63 - 42)]

==> A = √(63 × 18 × 24 × 21)

==> A = √571536

==> A = 756

∴ A = 756 cm²

Area of the triangle is 756 cm²