Question

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

Answer 1

third  side = 32 - 19 = 13,  semiperimeter = 16,  using  Herons  formula

Area =  root  of   16 * 3* 5*8 = root  1920 = 8 root 30 

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