Question

9. Using Heron's formula, find the area of a triangle two sides of which are8cm and 11 cm and the perimeter is 32 cm.​

Answer 1

Answer:

8√30 cm²

Step-by-step explanation:

Let a,b,c be the sides of the given triangle and 2s be its perimeter such that

a=8 cm, b=11 cm and 2s=32 cm

Now, a+b+c=2s

8+11+c=32

c=13

Therefore,

s−a=16−8=8,

s−b=16−11=5,

s−c=16−13=3

Hence, area of given triangle = √ s(s−a)(s−b)(s−c)

= √16×8×5×3

=8 √30 cm²