Scalene Triangle

A scalene triangle is a type of triangle that has three unequal sides and three unequal angles. In other words, no two sides of a scalene triangle are the same length, and no two angles are the same measure.

Properties of a Scalene Triangle

1. All three sides of a scalene triangle have different lengths.

2. All three angles of a scalene triangle have different measures.

3. The sum of any two sides of a scalene triangle is greater than the third side.

Formulas for Calculating Area and Perimeter

The formula to calculate the area of a scalene triangle is:

Area = (base * height) / 2

where base is the length of one side of the triangle, and height is the perpendicular distance from the base to the opposite vertex.

The formula to calculate the perimeter of a scalene triangle is simply:

Perimeter = side1 + side2 + side3

Example

For example, consider a scalene triangle with side lengths of 5 cm, 7 cm, and 9 cm. To find the area, we need to know the height, which can be calculated using trigonometry or other methods. Once we have the height, we can use the area formula to find the area of the triangle. To find the perimeter, we simply add up the three side lengths.

Study Tips

1. Practice identifying scalene triangles by looking at their side lengths and vertex angles.

2. Practice using the area and perimeter formulas for scalene triangles in different problems.

3. Understand the concept of inequality in scalene triangles, and how it relates to their side lengths and angles.

Summary

A scalene triangle is a triangle with three unequal sides and three unequal angles. It has unique properties and requires the use of specific formulas for calculating its area and perimeter.