Question

Find area of the triangle if its perimeter is 32 cms, if length of its two sides is
8 cms and 11 cms respectively.​

Answer 1

Answer:

Perimeter=8+11+x

32=8+11+x

32-19=x

13=x

Now, we know it's Semi-perimeter

Semi-perimeter = Perimeter/2

Semi-perimeter = 32/2

Semi-perimeter = 16 cm

Area of Triangle = √16(16 - 8) ( 16 - 11 ) ( 16 - 13 )

Area of Triangle = √16(8) ( 5 ) ( 3 )

Area of Triangle = √16 × 8 × 5 × 3

Area of Triangle = √2 × 8 × 8 × 5 × 3

Area of Triangle = √2 × 8 × 8 × 5 × 3

Area of Triangle = 8√2 × 5 × 3

Area of Triangle = 8√30

Thus The area of Triangle = 8√30 cm²

Answer 2

Answer:

8√30cm²

Step-by-step explanation:

Given,

Perimeter=32cm

side 1=8cm

side 2=11cm

So,

Semi perimeter = 16 cm

and side 3= 32-(8+11)

=>32-19

=>13 cm

now by using Heron's Formula,

Area of Triangle = √16(16-13)(16-11)(16-8)

=> √16*3*5*8

=>8√30 cm²