Question

Find the area of a triangle ,two sides of which are 11cm,8cm and the perimeter is 32cm.
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Answer 1

let third side be x

sum of all sides = perimeter of triangle

11 + 8 + x = 32

x = 32 - 19

x = 13

therefore, third side is 13cm

now we will find the area of the triangle by heron's formula which is √s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle.

semi-perimeter of this triangle = 32/2

= 16cm

area of the triangle = √16(16-8)(16-11)(16-13)

= √(16 × 8 × 5 × 3)

= √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 3)

= 2 × 2 × 2√(2 × 5 × 3)

= 8√30cm

Hope it help :)

Answer 2

Answer:

⇒Area = 8√30 cm²

Step-by-step explanation:

Sides of the ∆ABC, 8 cm & 11 cm. Also, the perimeter is 32 cm.

Firstly, finding the third side:

⇒ a + b + c = 2s

⇒ 8 + 11 + c = 32

⇒ 19 + c = 32

⇒ c = 32 - 19

⇒ c = 13 cm

Now,

Secondly, finding the area of the ∆ABC by Heron's formula:

We know that,

⇒ Area = √s ( s - a ) ( s - b ) ( s - c )

Therefore,

⇒1/2 ( a + b + c )

⇒1/2 ( 8 + 11 + 13 )

⇒ 1/2 ( 32 )

⇒ 16

⇒Area = √16 ( 16 - 8 ) ( 16 - 11 ) ( 16 - 13 )

⇒Area = √16 × 8 × 5 × 3

⇒Area = √ 8 × 8 × 30

⇒Area = 8√30 cm²