Question

The sides of a triangle are 3 cm, 5 cm and 6 cm. What is its area and perimeter?

Answer 1

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.

Answer 2

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 ,

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

$\sqrt{7(7 - 3)(7 - 5)(7 - 6) } \\ \sqrt{7 \times 4 \times 2 \times 1 } \\ \sqrt{7 \times2 \times 2 \times 2 \times1\: } \\ 2 \sqrt{7 \times 2} \\ 2 \sqrt{14} \\ 2 \times 3.74 \\ = 7.48$

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

Hence, The area and perimeter of triangle is 7.48cm^2 and 14cm