Question

Find the area of the triangle whose two sides are 18 cm, 10 cm respectively and perimeter is 42 cm.​

Answer 1

Answer :-

• Area of Triangle = 21√11 cm²

Given :-

• First Side (Side a) = 18 cm
• Second Side (Side b) = 10 cm
• Perimeter of triangle = 42 cm

To Find :-

• Area of Triangle = ?

Explanation :-

In order to find the area of the triangle first we need to find the Third Side (Side c) of the Triangle.

Let the Third Side (Side c) to be 'x' cm.

$\underline { \boxed { \bf \implies Perimeter \: of \: Triangle = Sum \: of \: all \: Sides }}$

$\rm \implies Side \: 1 + Side \: 2 + Side \: 3 = 42 \: cm$

$\rm \implies 18 + 10 + x = 42 \: cm$

$\rm \implies 28 + x = 42 \: cm$

$\rm \implies x = 42 - 28 \: cm$

$\underline { \boxed { \bf \implies x = 14 \: cm }}$

Now, Finding the Area of Triangle using Heron's Formulae.

$\underline { \boxed { \bf \implies Heron's \: Formulae = \sqrt{s (s -a) (s - b) (s-c) } }}$

Where,

• s = Semi - Perimeter of the Triangle
• a = First side of the Triangle
• b = Second side of the Triangle
• a = Third side of the Triangle

$\boxed { \bf \implies Semi \: Perimeter \: of \: Triangle = \frac{a + b + c}{2} }$

$\rm \implies \dfrac{18 + 10 + 14}{2}$

$\rm \implies \dfrac{42}{2}$

$\bf \implies 21 \: cm$

Now Substituting the values,

$\rm \implies \sqrt{s (s -a) (s - b) (s-c) }$

$\rm \implies \sqrt{21 (21 - 18) (21 - 10) (21 - 14) }$

$\rm \implies \sqrt{ 21 \times 3 \times 11 \times 7}$

$\underline { \boxed { \bf \implies 21 \sqrt{11} \: cm^2}}$

Hence, the area of the triangle is 21√11 cm².

@Agamsain

Answer 2

Question :

Find the area of the triangle whose two sides are 18 cm, 10 cm respectively and perimeter is 42 cm.

Given:

• Side of triangle (a) = 18 cm
• Side of triangle (b) = 10cm
• Perimeter of triangle = 42 cm

To find :

• Area of triangle
• Third side of triangle (c)

Solution:

➠Perimeter of triangle = sum of all the sides

42 = a + b + c

➥42 = 18 + 10 + c

➥42 = 28 + c

➥C = 42 - 28

➥c = 14 cm

➠Now, we need to find the area of triangle using heron's formula

$\boxed{\sf Heron's \: formula = \sqrt{s ( s - a )( s - b) ( s - c)}}$

➠Semi perimeter of triangle = (a + b + c) / 2

➥( 18 + 10 + 14) / 2

➥42 / 2

➥21 cm

Heron's formula = √s ( s - a )( s - b) ( s - c)

➥√21 ( 21 - 18 ) ( 21 - 10 ) ( 21 - 14 )

➥√21 ( 3 × 11 × 7 )

➥21√11 cm²

➠So, the area of triangle = 21√11 cm²