Question

find area of triangle with sides 5.5cm 7.5 cm and 30mm using heron s formula..plz answer fast..plzplz​

Answer 1

Given :

There is a one Triangle whose sides are given below :

• 5.5 Centimetres
• 7.5 Centimetres
• 30 Millimetre = 3 Centimetres

Heron s formula. ↴

$\boxed {\mathrm {A \: = \: \sqrt{S(S-a) \: S(S-b) \: S(S-c)} }}$

A = Area of Triangle

S = Semi Perimeter

a, b, c = Sides of Triangle

Now, We will find the Semi Perimeter :

$\boxed {\mathrm {Semi \: Perimeter = \dfrac{Perimeter}{2} }}$

$\boxed {\mathrm {Semi \: Perimeter = \dfrac{a + b + c}{2} }}$

$\sf \: Semi \: Perimeter \: \longrightarrow \: \dfrac{5.5 + 7.5 + 3}{2}$

$\sf \: Semi \: Perimeter \: \longrightarrow \: \dfrac{16}{2}$

$\sf \: \longrightarrow \: \dfrac{16}{2} = 18$

$\sf \: \longrightarrow \: So, \: the \: Semi \: Perimeter \: = 8 \: Cm \:$

After Finding the Semi Perimeter Now, We will. find the. Area of the Triangle.

$\boxed {\mathrm {A \: = \: \sqrt{S(S-a) \: (S-b) \: (S-c)} }}$

$\boxed {\mathrm {A \: = \: \sqrt{8(8-5.5) \: (8-7.5) \: (8-3)} }}$

$\boxed {\mathrm {A \: = \: \sqrt{8 \times 2.5 \times 0.5 \times 5} }}$

$\boxed {\mathrm {A \: = \: \sqrt{50} }}$

$\boxed {\mathrm {A \: = \: \sqrt{2 \times 5 \times 5} }}$

$\boxed {\mathrm {5 \sqrt{2} \: Centimetres {}^{2} }}$