Question

Mark the correct alternative in each of the following:
The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is

Options

• 225 cm²

• 225  \[\sqrt{3}\] cm²

• 225  \[\sqrt{2}\] cm²

• 450 cm² 

• none above 

Answer 1

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

`A = sqrt( s(s-a)(s-b)(s-c))`, where

`s = ( a+b+c)/2`

Therefore the area of a triangle say A, having sides 16 cm, 30 cm and 34 cm is given by

a = 16 cm ; b = 30 cm ; c = 34 cm

`s =  (a+b+c)/2 `

`s = (16 + 30 +34 )/2`

`s = 80/2`

s = 40 cm

Therefore the area of the triangle is 

`A = sqrt(40(40-16)(40-30)(40-34))`

`A = sqrt(40(24)(10)(6))`

`A = sqrt(57600)`

A = 240 cm²