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# Area of Triangle Formula

Last updated date: 09th Sep 2024
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## Area of a Triangle

A triangle is a polygon, which is a 2-dimensional object having 3 vertices and 3 sides. The area of a triangle can be determined using a simple formula that is used for solving questions or problems. If you want to find the area of the triangle then you must know the type of the triangle, length of the sides, and the height of the triangle. The area of a triangle is essentially a measurement of the area that is covered by the specific triangle. The area of the triangle is expressed in square units.

There are two formulas or ways in which the area of the triangle can be determined. The base multiplication with the height of the triangle divided by 2 and the second method is Heron’s formula for the area of the triangle.

### Definition and the Types of Triangles

The triangle has a 2D shape with three angles and three sides. The area of the triangle is the region that is enclosed within the triangle. There are potentially 4 types of triangles including the right-angled triangle, the Isosceles triangle, the Equilateral triangle, and the Scalene triangle. The right-angled triangle is the triangle having one angle of 90°, the isosceles triangle has two sides of equal length, the equilateral triangle has 3 equal sides and every angle is 60° and the scalene triangle has all unequal sides.

### Formula for the Area of the Triangle

The formula for the area of the triangle can be expressed as Area = A = ½ (b x h) square units, where h is the height of the triangle and b is the base of the triangle. The area of the triangle depends on the type of triangle. There are different formulas for a right-angled triangle, isosceles triangle, and equilateral triangle.

The area for the right-angled triangle is ½ x b x h.

The area of the isosceles triangle is ¼ x b x $\sqrt{4a^{2}-b^{2}}$.

The area of the equilateral triangle is $\sqrt{\frac{3}{4 \times a^{2}}}$.

Similarly, we have the heron's area of the triangle. The scalene triangle is the triangle where all three sides are basically unequal. To find the area of this triangle and other triangles, Heron’s formula can be used. If the scalene triangle has 3 sides with ‘a’, ‘b’, and ‘c’, then the heron’s formula can be stated as follows.

Area of the triangle A = $\sqrt{s(s-a)(s-b)(s-c)}$

### Solved Examples

The solved examples related to the area of the triangle help the students to strengthen their concept and understand the different types of questions as well as stepwise solutions to these questions. If you want to refer to the solved examples then you can check out the Vedantu notes related to this chapter here.

## FAQs on Area of Triangle Formula

1. What is the Difference Between Area and Perimeter?

The area can be defined as the space that is occupied by a specific shape. Whereas perimeter can be defined as the distance around that shape, which essentially means the boundary of the shape. The shapes having the same area can have varying perimeters, and the shapes having the same perimeters can have different areas. While the perimeter is measured as linear units, the area is measured as square units. This explains the significant difference between perimeter and area.

2. What is Heron's theorem in Mathematics?

The hero’s formula, also known as heron’s theorem in Mathematics, is named after Hero of Alexandria and it is used for finding the area of the triangle when length of all the three sides are known. The area of the triangle can be found by using the sides instead of the triangle height. Heron’s theorem helps in finding the triangle area when you don’t know the height of the triangle. Just put the side lengths in the heron’s formula and you can find the area.

3. How can you find the area of the isosceles triangle?

In an isosceles triangle, we know that two sides have equal lengths. Consider an example. We have an isosceles triangle having two equal sides ‘a’, and having the base as ‘b’. AD is the perpendicular which is drawn and which divides the base in 2 equal parts. Using the formula A = ½ x b x h, the formula for the area of isosceles triangle can be derived.  The area of the isosceles triangle is ¼ x b x √4a²-b². Using this formula, we can find the area of the isosceles triangle.

4. How do I study from the Vedantu notes on “Area of triangle formula”?