Area of a Triangle Calculator

Are you a student of architecture, civil engineering, mechanical engineering, mathematics, or physics? If yes, then you would have come across several topics where triangles have been extensively used. 

As an architecture or civil engineering student, you would be aware that construction sites often use triangles to make structures as strong and stable as possible. For instance, they are used in truss bridge construction where the forces are more distributed, and the structures are expected to bear a heavy load. Furthermore, as a Mathematics or Physics major, you would also study geodesic domes with their frames based on triangles. There are several instances where you need to study triangles and determine their area. 

The area of a triangle calculator is one of the many free online tools that determine the area of a triangle when the base and the height are provided to us. In addition to its reliability, this tool reduces time and delivers correct results in only a few seconds. This excellent resource will enable students to grasp difficult concepts or solve important problems at the click of a button. 

What is the Area of a Triangle?

When we think of geometry, a triangle is a two-dimensional form of an object with three sides and three vertices. Triangles are classified according to their sides and the angles within them. A triangle is a 2D shape, meaning it has an area and perimeter. The area refers to the space that lies within the triangle. Let us now learn how to find the area of a triangle.

Area of Triangle Formula

The area of a triangle can be determined using different formulas. For instance, Heron’s Formula is applied when the lengths of all three sides are known. Additionally, trigonometric functions can calculate the triangle area formula when two sides and the included angle are given. However, the most commonly used area of triangle formula is:

Triangle Area Formula = ½ x Base x Height

To understand the concept better, let us look at some area of triangle examples:

Example 1:

If one side of the triangle measures 8 cm, and the perpendicular height to this side is 5 cm, the area can be calculated as:

½ x 8 x 5 cm2 

= 20 cm2

Example 2:

For a triangle with a base of 10 m and a height of 7 m, the area is found as follows:

½ x 10 x 7 cm2

= 35 cm2

How to Use the Area of a Triangle Calculator?

We have outlined the steps on how to use the area of a triangle calculator:

• Step 1: Enter the values for the base and height into their respective fields.

• Step 2: Press the “Solve” button to calculate the area.

• Step 3: The calculated area of the triangle will appear in the output field.

Key Takeaways

Triangles hold significant importance in geometry, architecture, and practical applications in our day-to-day lives. Their distinct characteristics make them crucial in engineering and construction. Calculating the area of a triangle is a key mathematical concept with applications that go beyond the classroom. The area of a triangle calculator is a highly beneficial tool that offers a swift, dependable, and precise solution to compute areas while enhancing efficiency. By leveraging this tool, students can broaden their understanding of mathematical concepts and apply them confidently to real-life scenarios.

FAQs

What is the area of triangle formula?

The area of a triangle is given by the formula = ½ x base x height. 

How to find the base and height of a triangle?

To find the base and height of a triangle, the following approaches can be used:

1. When the area and height are given: The formula for the base is derived from the area formula, Area = ½ x Base × Height 

Therefore, if we rearrange the formula to find the base, the equation will be:

Base= 2 × Area/Height 

2. Similarly, when the area and base are given: The formula for the height can similarly be derived as:

Height = 2 × Area/Base

3. For an equilateral triangle: Since the base and height are interconnected, the area is expressed as:

Area = √3/4 a.

where a is the side of the triangle. Using this formula, the height and base can be calculated by substituting the side length or solving for a when the area is known.

How to find the area and perimeter of a triangle?

You can find the area and perimeter of a triangle by using the following formulas:

• Area of a Triangle Formula = ½ x Base × Height 

• Perimeter of a Triangle Formula = Side + Side + Side

How to find the area of a triangle without height?

To find the area of a triangle without the height, you can use Heron's formula, which is based on the lengths of the triangle's sides: 

Heron's formula = √s(s−a)(s−b)(s−c)

where a, b, and c are the sides of the triangle and 's' is the semi-perimeter; s = (a + b + c)/2.