Question

the sides of a triangle are 5cm, 6cm, and 7cm. find the area of triangle in approximately.

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.

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Answer 2

Hey mate,

As we know that,
this triangle is scalene triangle.
Solution : S = a+b×c/2
Here , 5+6+7/2
= 18/2
= 9 cm
Area of a triangle = √s(s-a)(s-b)(s-c)
= √9(9-5)(9-6)(9-7)
=. √9×4×3×2
=. √216
=. 14.69 square.cms
(approx).

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