Question

find the area of a triangle if it's sides are 1) 17 cm, 25 cmand26 cm​

Answer 1

Given :

• Sides of a triangle are 17 cm , 25 cm and 26 cm

To Find :

• The area of the triangle

Solution :

The area of a triangle is given by ,

$\\ \star \: {\boxed{\purple{\sf{a = \sqrt{s(s - a)(s - b)(s - c)} }}}}$

Where ,

• s is semiperimeter
• a , b and c are sides of the triangle

Semiperimeter of a triangle is given by ,

$\\ \star \: {\boxed{\purple{\sf{s = \frac{a + b + c}{2} }}}}$

Where ,

• a , b and c are sides of triangle

We have ,

• a = 17 cm
• b = 25 cm
• c = 26 cm

Substituting the values ,

$\\ : \implies \sf \: s = \frac{17 + 25 + 26}{2}$

$\\ : \implies \sf \: s = \frac{68}{2}$

$\\ : \implies{\underline{\boxed{\red{\sf{s = 34 \: cm}}}}}$

Now we have ,

• a = 17 cm
• b = 25 cm
• c = 26 cm
• s = 34 cm

Calculating the area of given triangle ,

$\\ : \implies \sf \: a = \sqrt{34(34 - 17)(34 - 25)(34 - 26)}$

$\\ : \implies \sf \: a = \sqrt{34(17)(9)(8)}$

$\\ : \implies \sf \: a = \sqrt{41616}$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{a = 204 \: {cm}^{2} }}}}} \: \bigstar$

$\\ \therefore \: {\underline{\sf{Hence \: , \: The \: area \: of \: the \: given \: triangle \: \: is \: \bold{ 204 cm^2}}}}$

Answer 2

✪ Formula to be used ✪

Area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Here:

s is the semiperimeter

a,b,c are the sides of the triangle.

Semiperimeter is basically the half of sum of all the sides.

✪ Assumptions ✪

Let us assume the sides :

a = 17 cm

b = 25 cm

c = 26 cm

✪ Process ✪

Now, we can say that semi perimeter will be:

$s=\frac{a+b+c}{2}$

Substituting a,b and c, we get:-

$s=\frac{17+25+26}{2}$

$\boxed{s=34cm}$

Substituting s,a,b and c in the area formula:-

$Area=\sqrt{34(34-17)(34-25)(34-26)}$

$=\sqrt{34(17)(9)(8)}$

$=204$

Thus, we can say that :-

$\huge\boxed{Area=204 cm2}$