Question

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

Answer 1

s=16

a=8

b=11

c=32-11-8=13

area=square root 16*(16-8)(16-11)(16-13)

=square root 16*8*5*3

=8 square root 30

Answer 2

QuEsTiOn :-

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

Answer :-

The area of traingle is 8√30 cm².

Given :-

Perimeter of triangle = 32 cm

Length of two sides of triangle are 8 cm and 11 cm

To Find :-

Area of traingle = ?

Solution :-

Consider the sides of traingle be a, b, c.

In Triangle,

First side = 8 cm

Second side = 11 cm

Perimeter = 32 cm

First Lets find the third side of a traingle :

✦ Third side = Perimeter - (First side of ∆ - Second side of ∆)

↠ Third side = 32 - (8 + 11)

↠ Third side = 32 - 19

↠ Third side = 13 cm

Now, we will find the Semi Perimeter of ∆ :

↠ Semi Perimeter = All sides of a ∆ ÷ 2

↠ Semi Perimeter = a + b + c ÷ 2

↠Semi Perimeter = 8 + 11 + 13 ÷ 2

↠ Semi Perimeter = 32 ÷ 2

↠ Semi Perimeter = 16 cm

Now, lets find the area of ∆ by using herons formula :

↠ Area = √s(s - a) (s - b) (s - c)

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

↠ Area = √16 × 8 × 5 × 3

↠ Area = 8√2 × 5 × 3

↠ Area = 8√30 cm²

Hence ,

The area of traingle is 8√30 cm².