Introduction on number of triangles in a hexagon:
The hexagon is a six sided polygon. In a regular polygon the side lengths are all equal. And the angles in a regular are all equal. The diagonals in a regular hexagon meet at the center of the hexagon to form triangles. Also the hexagons along with the sides form triangles inside the hexagon. In this article we will see in detail about the triangles in a hexagon.
Number of Triangles in a Hexagon:
In any polygon the diagonals connecting the opposite vertices are called as major diagonals while the diagonals connecting the other vertices with a vertex is called as a minor diagonal.
The major diagonals meet at the center of the polygon and divide the central angle such that the angle between the diagonals 60 degrees. Also the diagonals bisect the internal angle at a vertex. So the triangle formed by a side and the diagonals from its ends to the center will form a triangle with all the angles equal to 60 degrees. It is an equilateral triangle so the side length is equal to the length of the half of the diagonal. In a hexagon there will be six equal triangles.
The number of triangles formed by the diagonals from a given vertex = 6-2 = 4.
So the area of the triangle can be calculated as the sum of the area of the 6 triangles. In other words the area of the regular hexagon is equal to the product of a single triangle and 6. This can be written as,
Area of a regular hexagon = 6 * area of a single triangle inside the hexagon.
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Example Problems on Number of Triangles in a Hexagon:
1. Find the area of the hexagon if the area of a single triangle formed by the major diagonals in a hexagon is 9 square centimeters.
Solution:
The area of the hexagon = 6*area of a triangle.
So the area of the regular hexagon = 6*9 = 54 square centimeters.
Practice problems on number of triangles in a hexagon:
1. Find the area of the hexagon if the area of a single triangle formed by the major diagonals is 7.5 square centimeter.
Answer: 45 square centimeters
The hexagon is a six sided polygon. In a regular polygon the side lengths are all equal. And the angles in a regular are all equal. The diagonals in a regular hexagon meet at the center of the hexagon to form triangles. Also the hexagons along with the sides form triangles inside the hexagon. In this article we will see in detail about the triangles in a hexagon.
In any polygon the diagonals connecting the opposite vertices are called as major diagonals while the diagonals connecting the other vertices with a vertex is called as a minor diagonal.
The major diagonals meet at the center of the polygon and divide the central angle such that the angle between the diagonals 60 degrees. Also the diagonals bisect the internal angle at a vertex. So the triangle formed by a side and the diagonals from its ends to the center will form a triangle with all the angles equal to 60 degrees. It is an equilateral triangle so the side length is equal to the length of the half of the diagonal. In a hexagon there will be six equal triangles.
The number of triangles formed by the diagonals from a given vertex = 6-2 = 4.
So the area of the triangle can be calculated as the sum of the area of the 6 triangles. In other words the area of the regular hexagon is equal to the product of a single triangle and 6. This can be written as,
Area of a regular hexagon = 6 * area of a single triangle inside the hexagon.
I am planning to write more post on math word problems solver, solve system of linear equations. Keep checking my blog.
Example Problems on Number of Triangles in a Hexagon:
1. Find the area of the hexagon if the area of a single triangle formed by the major diagonals in a hexagon is 9 square centimeters.
Solution:
The area of the hexagon = 6*area of a triangle.
So the area of the regular hexagon = 6*9 = 54 square centimeters.
Practice problems on number of triangles in a hexagon:
1. Find the area of the hexagon if the area of a single triangle formed by the major diagonals is 7.5 square centimeter.
Answer: 45 square centimeters
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