Question

5. Find the area of a triangle where two side are 18cm and 10cm and the perimeter is 42 cm.
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Answer 1

Given: Two sides of the ∆ are 18 cm and 10 cm. & the perimeter is 42 cm.

Let's Consider, the third side be x cm.

★ Peri. of ∆ = (a + b + c)

➟ ⠀18 + 10 + x = 42

➟ ⠀28 + x = 42

➟ ⠀x = 42 – 28

➟ ⠀x = 14

The third side of the triangle is 14 cm.

If the perimeter of the triangle is 42 cm then semi perimeter of the triangle would be 21 cm. i.e ( s ) = 21 cm.

• H e r o n's F o r m u l a :

➟ ⠀Ar. = √(s – a) (s – b) (s – c)

➟ ⠀Ar. = √(21 – 18) (21 – 10) (21 – 14)

➟ ⠀Ar. = √7 × 3 × 3 × 11 × 7

➟ ⠀Ar. = 7 × 3√11

➟ ⠀Ar. = 21√11

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

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Answer 2

Given Data :

 

• Two sides of the ∆ are 18 cm and 10 cm .
• The Perimeter is 42 cm.

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Let , the third side be x cm.

Perimeter of ∆ = (a + b + c)

➻⠀18 + 10 + x = 42

➻⠀28 + x = 42

➻ ⠀x = 42 – 28

➻ ⠀x = 14

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• The third side of the triangle is 14 cm.

_________________________

If the perimeter of the triangle is 42 cm

then ,

semi perimeter of the triangle would be 21 cm.

i.e., (s) = 21 cm

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By Heron's formula :

➻⠀Area of ∆ = √(s – a) (s – b) (s – c)

➻ ⠀Area of ∆ = √(21 – 18) (21 – 10) (21 – 14)

➻ ⠀Area of ∆ = √7 × 3 × 3 × 11 × 7

➻ ⠀Area of ∆ = 7 × 3√11 = 21√11 cm

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➻ ⠀Area of ∆ = 21√11 cm

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▪ The Area of the Triangle is 21√11 cm²