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In maths, a polygon is a part of geometry which is a structure formed by adjoining straight lines. Some straight segments connect to forms a polygonal chain or circuit. It can also be said as a rigid plane bound by two or more circuits.

Area of a polygon can be irregular and regular. Square, rectangle, triangle, pentagon, hexagon, are the primary forms of a polygon. Since the size remains similar, it becomes easier to determine the area of regular polygons.

One can see that to find the area of a square, the length of one side must be known since its sides are equal.

Students in this segment will learn about the area of polygon formula and its application. The area here refers to a space occupied within a figure or even object. An individual needs to proceed with standard measurement taking a square unit that is square meters. For shapes like rectangles, triangles, squares, trapeziums and others, there are separate formulas. But an irregular polygon requires a combination of two or more polygons for area calculation.

The area of a polygon is defined as the region occupied irrespective of its shape, like a parallelogram, triangle, quadrilateral, square, rectangle or rhombus. It is always a two-dimensional plane.

The formulas for areas of unlike polygon depends on their respective shapes. Just as one requires length, base and height to find the area of a triangle. Similarly, different shape requires a specific formula.

Let us check the ways to find the formula of polygons and its areas.

It is essential to know that the area of a polygon not standard as its formula is not definite. Therefore, one needs to divide figures into squares, trapezium, triangles, etc. It is done to envisage the given geometry which is a combination. One can easily calculate the area for each section by adding any given data.

Below are some ways to find the area of types of polygon shapes.

The area of an equilateral triangle is ideally the space that occupies a plane which is two dimensional. An equilateral triangle has all equal sides so the sum of interiors will be 60°. Therefore, the area of an equilateral triangle will be calculated when one side or length is provided.

Area of Equilateral Triangle is calculated with the formula (√3/4)a.

A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of additional measures. However, the sum of all the interior angles is always equal to 180 degrees.

The area of a scalene triangle can be found by taking its base ‘b’ and height ‘h’ which refers to -

A =1/2×b×h units in a square.

A pentagon is a form of a two-dimensional shape which has five sides. It is also called as polygon due to its five sides which can be both irregular and regular. The angles and sides of this shape are always parallel to each other. The total sum of inside angle of a pentagon is always 108 degrees while the outside is 72 degrees.

Area of a regular pentagon is the area engaged by a perimeter and plane. This is also the sum of its all sides.

The number of diagonals in any pentagon is five so the solution will be {n*(n-4)}/2. Here n symbolises the number of sides.

In a pentagon, we know that the number of sides is equal to 5, so ‘n’ becomes five as well.

Therefore, Number of diagonals of a pentagon by applying area of pentagon formula is [5(5-4)]/2

Which gives (5 x 1)/2 that is 2.5

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FAQ (Frequently Asked Questions)

1. What is the Area of an Equilateral Triangle Whose Perimeter is 15 cm?

Ans. We are given perimeter of an equilateral triangle to be 15 cm

By following the perimeter of an equilateral triangle, we find 3a, where “a” is the side of the equilateral triangle. After using perimeter, we find the side of an equilateral triangle to be

3a is 15

a = 5

Thus, the length of the side is 5 cm.

To find the area of an equilateral triangle one can also use the formula Area √3 a2/ 4 sq. units

= √3 (5)2/ 4 cm²

= 6.25√3 cm²

Therefore, the area of the given equilateral triangle is 6.25√3 cm².

2. What is an Isosceles Triangle?

Ans. An isosceles triangle has its two sides equal. Its angles on the opposite side are equal. Generally, a triangle is a polygon with three vertices and three sides. An isosceles triangle has variable sides and angles and two equal sides. An isosceles triangle has two matching sides.

An isosceles triangle is classified into different types, namely, acute Isosceles triangle, isosceles right triangle and obtuse Isosceles triangle. Base to a topmost vertex of the triangle is used to measure the altitude of an isosceles triangle.

3. What is a Hexagon?

Ans. A hexagon has both the features of equiangular and equilateral. It is cyclic and peripheral. It has a general length that is equal in size and circumcircle. The bounded circle is also found to be similar to apothem. Here the diagonals with long side are joined to opposite vertices which are two times the length of a side.

This gives the idea that vertex in a triangle of a general hexagon at the centre is equilateral. Also, the side of a hexagon can be divided into six equilateral triangles.