How to Find the Area of a 3-sided Closed Polygon?

A 3 sided closed polygon that is joined end to end is referred to as a triangle. It consists of three angles, three vertices, and three sides. When a child is introduced to this topic, he has to learn about the area of triangle and other associated concepts. In this article, we will learn more about how to calculate the area of a triangle using different methods.

Fun Facts on Triangles

1. Architects are slowly shifting towards incorporating triangles into their construction plans. It is easier to work with rectangles; however, triangular constructions prove to be stronger and more resistant to earthquakes.
2. Suppose you have a rectangle. If you draw a line from one corner to the opposite corner to form the diagonal, it divides the rectangle into two similar triangles.
3. All the angles of a triangle must sum up to 180 degrees.
4. The sum of the lengths of two sides of a triangle must be larger than the third side. Conversely, the difference between the lengths of any two sides of a triangle must be lesser than the third side.

Different Types of Triangle

1. Equilateral Triangle – A triangle in which all sides are equal.
2. Isosceles Triangle – A triangle in which only two sides are equal.
3. Scalene Triangle – A triangle in which none of the sides are equal.
4. Acute Triangle – A triangle in which all angles are less than 90 degrees.
5. Right Triangle – A triangle with one angle measuring 90 degrees.
6. Obtuse Triangle – A triangle in which one angle measures more than 90 degrees but less than 180 degrees.

Methods to Calculate the Area of a Triangle

1. Heron’s Formula

This is the most basic formula to find the area of a triangle when all three sides are known. Heron of Alexandria came up with this formula. Suppose we have a triangle MGK with side lengths given by m, g, k.

Then we first find the semi perimeter of the triangle given by

s = ( m + g + k) / 2

Using this, we get the formula for the area of a triangle

A =

2. Base Height Formula

When you have a triangle whose height and length of the base are known, and the corresponding sides are known, then we can use the base height formula to find the area of the triangle. Suppose we have a triangle MGK with height given by h, and length of the base is given by b then formula used is

Area of triangle = ½ (base)(height)

= ½ (b)(h)

3. Trigonometric Formula

If you know the length of any two sides and the angle opposite to them, then trigonometric formulas can be used. Suppose we have a triangle MGK with side lengths given by m, g, k, and angles are given by M, G, K then we have

• A(MGK)= ½ gk sin M
• A(MGK)= ½ mk sin G
• A(MGK)= ½ mg sin K

Conclusion

Triangles can prove to be a complicated topic; hence, it is best for kids to take the services of a good online institution such as Cuemath. The certified tutors at Cuemath believe in guiding kids through problem sums rather than just giving them the answer. This helps children to build up their cognitive and critical thinking abilities. They use several resources to deliver a fun-filled and impactful lecture. Hopefully, this article gives you an idea of which type of formula can be applied to what question and where to go when you want to sharpen your skills.