# Some Interesting Properties of a Triangle

The total space that is occupied inside a triangle can be stated as the area of triangle. A triangle is made up of three sides that may be congruent to each other. The area that is occupied by the three sides of the triangle is known as the area of a triangle.

A triangle is a two-dimensional mathematical figure. The mathematical formula to calculate the area of a triangle is, 1/2 * b * h where ‘b’ is the base of the triangle and ‘h’ is the height of the triangle.

A triangle is further classified into various types based on the length of the sides and their angles of it. They are the scalene triangle, acute triangle, and equilateral triangle. The formula mentioned for the area of a triangle is applicable for all the types of triangles discussed above. You must remember that the base and height of the triangle are perpendicular to each other.

The following points mentioned below analyze the properties of a triangle.

- A triangle is made up of three sides and angles. Based on these attributes, they are further classified into various types.
- The sum of the angles of a triangle is always equivalent to 180 degrees.
- The sum of exterior and interior angles always results in a supplementary value i.e. 180 degrees.
- The hypotenuse is the longest side of a right-angled triangle. The other two sides i.e. height and base are upright to each other.

## Examples Based on the Area of the Triangle

To recall, the mathematical formula to calculate the area of a triangle is, 1/2 * b * h where ‘b’ is the base of the triangle and ‘h’ is the height of the triangle.

**Example 1: **Calculate the area of a triangle, when the length of the base and height is equivalent to 16 cm and 6 cm respectively.

**Solution**:

Given that,

Height of the triangle = 6 cm

The base of the triangle = 16 cm

The formula is given for the area of the triangle = 1/2 * b * h.

1/2 * 4 * 6 = 1/2 * 96.

1/2 * 96 = 48 cm square units.

Hence, the area of a triangle is 48 cm square units.

## What are 3d Shapes?

A mathematical figure or object is classified into two types based on the dimensions. They are 2d shapes or two-dimensional shapes and 3d shapes or three-dimensional shapes. Two-dimensional shapes consist of length and breadth whereas a three-dimensional shape consists of length, breadth, and height.

Some examples of 2d shapes are square, rectangle, trapezoid, triangle, and so on.

Some examples of 3d shapes are cubes, cuboids, cones, cylinders, and many more. The other significant terms that are related to the 3d shapes are vertices, edges, and faces. You may face these terms while you study about 3d shapes.

Suppose, you need to find the area of a field that resembles the shape of a triangle. To accomplish this work, you need to know about the area of the triangle. Hence, we can say that knowing about the area of a triangle is a must. Similarly, you may encounter various real-life objects that are three-dimensional. If you want to study more about the area of the triangle and 3d shapes, you may visit Cuemath.