Question

4. Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm
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Answer 1

⇝ Given :-

For A Triangle ;

• First Side = 18 cm

• Second Side = 10 cm

• Perimeter = 42 cm

⇝ To Find :-

• Area of the Triangle.

⇝ Solution :-

Here,

• First Side = a = 18 cm

• Second Side = b = 10 cm

• Perimeter = P = 42 cm

• Semi - Perimeter = s = $\bf\dfrac{42}{2}$ = 21 cm

❒ Finding Third Side :-

Let Third Side be = c

We Know,

$\rm Perimeter = Sum \: of \: All \: Sides$

$\rm:\longmapsto42 = 18 + 10 + c$

$\rm:\longmapsto c = 42 - 18 - 10$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf c = 14 \: cm} }}}$

❒ Finding Area :-

To Calculate Area when three sides are given we will use Heron's Formula which is :

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}$

where

• a , b and c are sides of Triangle

• s = Semi - Perimeter

⏩ Putting Values In Formula ;

$\small \rm Area = \sqrt{21(21 - 18)(21 - 10)(20 - 14) \: }$

$= \sqrt{21 \times 3 \times 11 \times 7 \: }$

$= \sqrt{4851}$

$= 21 \sqrt{11}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf Area=69.64 \: cm^2} }}}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{\text Area\:of\:\text Triangle = 69.64 \: {cm}^{2} }}}}}$

Answer 2

Given :-

Side of triangle = 18 cm and 10 cm

Perimeter = 42 cm

To Find :-

Area

Solution :-

Let the third side be x

Perimeter = x + y + z

42 = x + 18 + 10

42 = x + 28

42 - 28 = x

14 = x

Now

Semiperimeter = Perimeter/2

Semiperimeter = 42/2

Semiperimeter = 21 cm

Area = √s(s - a)(s - b)(s - c)

Area = √21(21 - 18)(21 - 10)(21 - 14)

Area = √21(3)(11)(7)

Area = √4851

Area = 21√11 cm²

Take √11 as 3.31

Area = 21 × 3.31

Area = 69.51 cm²

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