Question

Find the area of triangle whose sides are 7cm ,4cm,5cm

Answer 1

Answer:

The answer in the attachment of this answer⬆️⬆️⬆️⬆️.............☺

Step-by-step explanation:

${\huge{\overbrace{\underbrace{\purple{❤❤}}}}}$

Answer 2

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 :-

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