The sides of a triangle are 3 cm, 5 cm and 6 cm. What is its area and perimeter?
Answers
This problem can be solved by Heron’s Formula,
A=√s(s−a)(s−b)(s−c)
where S (0.5*(a+b+c)) is one half of the perimeter of the triangle, sometimes called the semi-perimeter.
A is the area of the triangle
And a,b,c are the sides of the triangle
So if a=3 cm ,b=5 cm and c=6 cm
thus , Using Heron’s Formula we get the semi-perimeter as 7 cm
and the area as
A= sqrt(7*(7–3)(7–5)(7–6))
thus A= sqrt(7*4*2*1)=sqrt(56)=7.48 sq. cm.
thus the area of the triangle with side 3 cm,5 cm and 6 cm is 7.48 sq cm.
Solution :-
The sides of triangle are 3cm, 5cm and 6cm
Now,
We have to find the area of triangle
Therefore,
Semiperimeter = a + b + c / 2
Semiperimeter = 3 + 5 + 6 / 2
S = 14/2 = 7
Now,
By using Heron's Formula ,
Thus, The area of a triangle is 7.48cm^2
Now,
Perimeter of triangle = a + b + c
Therefore,
Perimeter of triangle = 3 + 5 + 6 = 14cm