Question

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

Answer 1

$\large \tt AHOY!! \:$

let the sides of the triangle be a, b and c

given length of the sides of the triangle are :-

a = 8cm

b = 11cm

c = ?

perimeter of the triangle is given = 32cm

since the sum of all three sides of a triangle is it's perimeter

=> a + b + c = 32cm

=> 8 + 11 + c = 32cm

=> 19 + c = 32cm

=> c = 32 - 19

=> c = 13cm

now we will find the area of the triangle by heron's formula which is √s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle.

semi-perimeter of this triangle = 32/2

= 16cm

area of the triangle = √16(16-8)(16-11)(16-13)

= √(16 × 8 × 5 × 3)

= √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 3)

= 2 × 2 × 2√(2 × 5 × 3)

= 8√30cm²

$\large \tt HOPE \: THIS \: HELPS!! \:$

Answer 2

Answer:

8$\sqrt{30}$

Step-by-step explanation:

s(semi-perimeter) and a,b and c are sides of a triangle

using Heron's formula,

$\sqrt{s(s-a)(s-b)(s-c)}$

a=8 cm

b=11 cm

c=32-(8+11)$\sqrt{(16(8)(5)(3)}$

c=32-19

c=13 cm

s=8+11+13/2=16

$\sqrt{16(16-8)(16-11)(16-13}$

$\sqrt{(16(8)(5)(3)}$

$\sqrt{2*2*2*2*2*2*2*5*3}$

2*2*2*$\sqrt{30}$

8$\sqrt{30}$