\tt{\bf{ Area =  9.76 \; {CM}^{2} }}

Therefore,

☞ Area of the ∆ = 9.76 cm²

Diagram :-

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Explanation:

Answers

THE BRAINLIEST ANSWER!

MisterIncredible

MisterIncredibleBrainly Stars

Given :-

Measurements of the triangle are 7cm , 4 cm and 5 cm

Required to find :-

Area of the triangle ?

Formulae used :-

\rm{\bf{s = \dfrac{ a + b + c }{ 2 } }}

\tt{\bf{ Area = \sqrt{ s ( s - a )( s - b )( s - c ) }}}

Solution :-

Given information :-

Measurements of the triangle are ; 7cm , 4cm & 5 cm

We NEED to find the area of the triangle .

In order to find it's area we should USE ; Herons formula

So,

Let's find the semi - perimeter of the given triangle .

USING the formula ;

\rm{\bf{s = \dfrac{ a + b + c }{ 2 } }}

\rm{\bf{s = \dfrac{  7 + 4 + 5 }{ 2 } }}

\rm{\bf{s = \dfrac{ 16 }{ 2 } }}

\rm{\bf{s = 8 }}

Hence,

Semi - perimeter of the ∆ is 8

Using Heron's formula ;

\tt{\bf{ Area = \sqrt{ s ( s - a )( s - b )( s - c ) }}}

Here ,

s = semi - perimeter

a , b , c = Three sides of the triangle

Substituting the values ;

\tt{\bf{ Area = \sqrt{ 8 ( 8 - 7  )( 8 - 4 )( 8 - 5 ) }}}

\tt{\bf{ Area = \sqrt{ 8 ( 1 )( 4 )( 3 ) }}}

\tt{\bf{ Area = \sqrt{ 8 \times 12  }}}

\tt{\bf{ Area = \sqrt{ 96 }}}

\tt{\bf{ Area = \sqrt{ 16 \times 6 }}}

\tt{\bf{ Area = \sqrt{ 16 } \times \sqrt{6} }}

\tt{\bf{ Area = 4 \sqrt{ 6 }}}

\tt{ ( \; \because \;  \sqrt{6} \; = 2.44 )  }

This implies,

\tt{\bf{ Area = 4 \times 2.44 }}

\tt{\bf{ Area =  9.76 \; {cm}^{2} }}

Therefore,

☞ Area of the ∆ = 9.76 cm²

Diagram :-