Table of Contents

- 1 What is an integer in a triangle?
- 2 What is an integer length geometry?
- 3 What are superhero triangles?
- 4 How do you find the Semiperimeter of a triangle?
- 5 How to find the area of a triangle with consecutive integers?
- 6 What is the difference between integer triangle and rational triangle?
- 7 How do you find the number of triangles in a semicircle?

## What is an integer in a triangle?

An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers. All other sections refer to classes of integer triangles with specific properties.

## What is an integer length geometry?

Integer Geometry is the geometry of points that are pairwise integer distances apart. An integer polygon is a convex set of n points in the plane such that no three points are collinear and the distance between any two points is an integer.

**How do you find the area of a Heronian triangle?**

Every angle of a Heronian triangle has a rational sine. This follows from the area formula Area = (1/2)ab sin C, in which the area and the sides a and b are integers, and equivalently for the other angles.

### What are superhero triangles?

These are right-angle triangles that have all integer sides. The smallest is the {3,4,5} triangle. Heroic (Heronian) triangles are triangles that have integer length sides and an integer area. They can also be scalene, such as {5,29,30}, which can’t be made from gluing together two Pythagorean triangles.

### How do you find the Semiperimeter of a triangle?

The semi perimeter of a triangle can be calculated if the length of the three sides is given. The formula for the semi perimeter of a triangle is S = (a + b + c)/2, where ‘a’, ‘b’, ‘c’ are the three sides of the triangle.

**What is herons formula used for?**

In geometry, Heron’s formula (sometimes called Hero’s formula), named after Hero of Alexandria, gives the area of a triangle when the length of all three sides are known. Unlike other triangle area formulae, there is no need to calculate angles or other distances in the triangle first.

## How to find the area of a triangle with consecutive integers?

The general formula for the area of a triangle whose side lengths are consecutive integers can be derived as follows: let x equal the length of the smallest side. The other two sides are then x + 1 and x + 2, and s (half the sum of the sides) is $\\frac{3x + 3}{2}$.

## What is the difference between integer triangle and rational triangle?

Integer triangle. An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers. A rational triangle can be defined as one having all sides with rational length; any such rational triangle can be integrally rescaled (can have all sides multiplied by the same integer,…

**How to find the area of a triangle with three sides?**

The general formula for the area of a triangle whose side lengths are consecutive integers can be derived as follows: let x equal the length of the smallest side. The other two sides are then x + 1 and x + 2, and s (half the sum of the sides) is $\\frac{3x + 3}{2}$. Subtracting each of the three sides from s and multiplying out gives.

### How do you find the number of triangles in a semicircle?

The number of integer triangles (up to congruence) with given largest side c and integer triple ( a , b , c) that lie on or within a semicircle of diameter c is the number of integer triples such that a + b > c , a2 + b2 ≤ c2 and a ≤ b ≤ c. This is also the number of integer sided obtuse or right (non- acute) triangles with largest side c.