Question

Class 9th
Mathematics
Chapter 12 - Heron's Formulas
Formulas Needed . Give 1 example for each Formuals

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Quality answer with good explanation will be Brainliest .​

Answer 1

Answer:

By Heron's formula,

first,s=a+b+c/2 where a,b,c are the sides of the triangle. After that, apply the following formula of triangle:-

Area of∆=√s(s-a)(s-b)(s-c)

#other formulas related to triangle are following:

area of an euilateral triangle=√3/4a square

area of an isosceles triangle=b/4√4a square-b square

area of a rhombus= 1/2×product of its diagonals

area of a square=side× side

Step-by-step explanation:

Hope it will help you.

If u want some more formulae,take the help of book

Answer 2

Answer :-

Formula :-

Heron's formula is a method used to find the area of a triangle when it's 3 sides are given.

According to the formula,

In order to find the area of the triangle, we first have to find it's semi - perimeter.

PERIMETER :-

Perimeter refers to the total length of the boundry of any figure. It is calculated by adding all the values of the figure's sides.

SEMI PERIMETER :-

Semi perimeter refers to ½ of the perimeter.

$\boxed{ \sf semi \: perimeter = \dfrac{ a+ b + c}{2} }$

'a', 'b' and 'c' here refer to the 3 sides of the triangle.

When the value of the semi perimeter is found,

The area of the figure will be :-

$\boxed{\sf \sqrt{s (s - a) (s - b) ( s-b)} }$

The sides of the triangle are subtracted from the semi perimeter and then multipled with the semi perimeter. The root of this value is the area of the traingle.

Example :-

Let us take an example to understand this formula.

Let,

• a = 4cm
• b = 13cm
• c = 15cm

Now that we have the values of the triangle's sides, let us find the semi perimeter of the triangle

$\implies \sf semi \: perimeter = \dfrac{4 + 13+ 15}{2}$

$\implies \sf semi \: perimeter = 14cm$

By substituting this value,

$\implies \sf \sqrt{(16) \times (16 - 4) \times (16 - 13) \times (16 - 15)}$

$\implies \sqrt{16 \times 12\times 3 \times 1}$

$\implies \sf \sqrt{576} {cm}^{2}$

$\implies \sf {24cm}^{2}$

Hence the area of the triangle is 24cm²