How to Find the Area of a Scalene Triangle?

Any polygon that is closed and has three vertices, three edges, and three angles is called a triangle. There are many different types of triangles based on the classification of sides and angles. Additionally, there are several concepts, such as the area of scalene triangle that must be thoroughly understood by kids. In this article, we will learn more about triangles with a special focus on scalene triangles.

Classification of triangles On the Basis of Sides

Equilateral Triangle

All the sides are of equal measure, and the triangle is equiangular. This implies that each angle measures 60 degrees.

Isosceles Triangle

This triangle has two equal sides. As the two sides are equal hence, the angles opposite to these sides are also equal.

Scalene Triangle

A scalene triangle is one in which all three sides are of unequal measure. This also means that none of the angles are of equal measure. If the two sides of a triangle are not congruent, then it can be classified as a scalene triangle. An example of a scalene triangle is the sail of a boat. As all the sides are of different measure thus, when it is raised, the sail forms a scalene triangle.

Properties of a Scalene Triangle

• The sides’ lengths are not equal.
• The angles are also of unequal measure.
• There is no point or line of symmetry. This implies that it cannot be broken down into two identical halves.
• The internal angles can be any of the three angles – acute, obtuse, or right.
• If all the angles are less than right angles, the center of the circumscribing circle will be inside the triangle.
• If all the angles are greater than right angles, the center of the circumscribing circle will be outside the triangle.

Area of a Triangle

The following techniques can be used to find the area of a scalene triangle depending upon the known and unknown parameters.

1. Heron’s Formula

Herons formula can be used to calculate the area of a scalene triangle. The requirement to apply this formula is that we know all the sides of the triangle. Suppose we know the three sides of a triangle given by a, p, and l; then, according to the formula, we need to find the semi perimeter before proceeding to determine the area of the triangle.

• Semi perimeter, s = (a + p + l) / 2
• Area of the scalene triangle = √[s (s – a) (s – p) (s – l)]

2. Height Base Formula

If we know the height of the scalene triangle and the corresponding base, we can use this formula as it is easier to apply. The height is a perpendicular dropped from a vertice to one side of the triangle that is known as the base. The following formula is known as the height base formula.

Area of a scalene triangle = ½ × (height) × (base).

Conclusion

There are other methods to find the area of a triangle, such as trigonometric formulas when we know certain angles. Additionally, the law of cosines is useful to calculate an unknown third side. Kids can find it confusing to apply these formulas to questions, especially if they do not possess the speed and accuracy of calculations. To combat this problem, they can turn to a platform such as Cuemath that helps kids instill a robust mathematical foundation. The certified experts use several resources such as worksheets, workbooks, puzzles, etc., to ensure that kids have a fun learning experience while getting access to the best quality of education. Begin your journey with Cuemath today!