Question

Area of Triangle 25cm, 25cm, 34cm (Using Heron's Formula Only)

Answer 1

Given :-

Side of triangle = 25 cm, 25 cm and 34 cm

To Find :-

Area

Solution :-

We know that

S = a +  b + c/2

S = 25 + 25 + 34/2

S = 84/2

S = 42 cm

Now

Area = √s(s - a)(s - b)(s - c)

Area = √42(42 - 25)(42 - 25)(42 - 34)

Area = √42(17)(17)(8)

Area = 17√42(8)

Area = 17√336

Area = 17 × 4√21

Area = 68√21 cm²

Answer 2

$\underline{ \pink{ \rm GIVEN \: \: DATA\: \: : }}$

Sides of Triangle :-

25cm , 25cm , 34cm

$\underline{ \purple{ \rm TO \: \: FIND \: \: : }}$

Area of Triangle

$\underline{ \red{ \rm SOLUTION \: \: : }}$

First, Finding semi perimeter(s)

$\green{ \boxed{ \boxed{ \color{darkblue} \rm s = \frac{a \: + \: b \: + \: c}{2} }}}$

substituting values,

$\rm s = \frac{25 + 25 + 34}{2}$

$\rm s = \frac{84}{2}$

$\boxed{ \color{gold} \rm s = 42}$

and, we know that

the formula to find Area of Triangle,

$\boxed{ \boxed{ \color{brown}{ \rm Area = \sqrt{s(s - a)(s - b)(s - c )}}}}$

by substituting values,

$\rm Area = \sqrt{42(42 - 25)(42 - 25)(43 - 34)}$

$\rm Area = \sqrt{42(17)(17)(9)}$

$\rm Area = \sqrt{109242}$

$\boxed{ \boxed{ \color{springgreen}\rm Area = 330.5 \: {cm}^{2} }}$

$\underline{ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}$

$\therefore \rm \rm Area \: \: of \: \: \triangle = \orange{ 330.5 \: {cm}^{2} }$