Question

Find the area of following triangles by heron 's formula and also find the length of the height corresponding its largest side; 18mm, 24mm ,32mm

Answer 1

Answer:

According to the Heron's formula, Area (A) of the triangle having sides a,b,c units is  

A=  /sqrt{x}s(s−a)(s−b)(s−c)

​ where

s=  2 (a+b+c )

​  

 

For the given triangle,

a=18 cm  

b=24 cm  

c=30 cm  

s=  2 18+24+30

​  

=36

A=  36(36−18)(36−24)(36−30)

​  

 

A=  36×18×12×6

​  

A=  216×216

​  

=216  cm  2

 

Smallest side =18 cm

Area of the triangle =  2 1×base×altitude=216  2 1  ×18× altitude=216

Altitude =  9 216

​  

=24 cm