Question 1

What is Heron's formula and when is it used?

Accepted Answer

Heron's formula calculates the area of a triangle from only its three side lengths, without needing to know the height. Area = sqrt(s(s-a)(s-b)(s-c)) where s = semi-perimeter.

Question 2

How do I verify that lengths form a valid triangle?

Accepted Answer

The sum of any two sides must be greater than the third side. For example: a+b > c, a+c > b, b+c > a.

Question 3

What is the difference between the inscribed and circumscribed circles?

Accepted Answer

The inscribed circle (incircle) lies inside the triangle and touches all three sides, while the circumscribed circle passes through all three vertices of the triangle.

Question 4

How do I calculate the height of a triangle from its area?

Accepted Answer

Area = (base × height) / 2, so height = (2 × Area) / base.

Question 5

What is a right triangle and how do I identify it?

Accepted Answer

A right triangle has one 90-degree angle and satisfies the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the other two sides.

Triangle Calculator