The area of triangle with given two sides 18cm and 10cm respectively and perimeter equal to 42 cm is: Question The area of triangle with given two sides 18cm and 10cm respectively and perimeter equal to 42 cm is: in progress 0 Math Serenity 2 months 2021-10-09T18:07:56+00:00 2021-10-09T18:07:56+00:00 2 Answers 0 views 0

## Answers ( )

Given:

Perimeter of triangle is 42 cm.

Measure of two sides of triangle are 18 and 10 cm respectively.

To Find:

What is the area of triangle?

Solution: Let the third side of triangle be x cm. Therefore,

➯ Sum of all sides = Perimeter

➯ 18 + 10 + x = 42

➯ x = 42 – 28

➯ x = 14 cm { Third sides of triangle }

Now, For finding area of ∆ we will use Heron’s Formula.

First find the Semi-Perimeter (s)

➬ s = (Sum of all sides / 2)

➬ s = (42/2)

➬ s = 21

★ Formula = √s(s–a) (s–b) (s–c) ★

➛ √21 (21 – 18) (21 – 10) (21 – 14)

➛ √21 (3) (11) (7)

➛ √3 7 3 11 7

➛ 3 7 √11

➛ 21√11 cm²

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Given,

Side a=18cm

Side b=10cm

Perimeter=42cm=a+b+c

:. Putting value

42=18+10+c

42=28+c

42-28=c

14=c

Now,

S=(a+b+c)/2

:. Putting value

S=42/2

S=21

Now according to Heron’s formula-

Area of a triangle

=√{s(s-a)(s-b)(s-c)}

:. Putting value

=√{21(21-18)(21-10)(21-14)}

=√{21(3)(11)(7)}

=√4851

=21√11cm²

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