To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon’s center to the midpoint of any side that is perpendicular to that side.
What is the formula for the area of polygon?
The formula to calculate the area of a regular polygon is, Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula, Apothem = [(length of one side)/{2 ×(tan(180/number of sides))}].
How do you find area of a pentagon?
The basic formula for the area of a regular pentagon is, Area of pentagon = 1/2 × p × a; where ‘p’ is the perimeter of the pentagon and ‘a’ is the apothem of a pentagon.
What is the area of polygon class 8?
Area of polygon=102cm2+25.5cm2=127.5cm2 . Hence, the area of the polygon is 127.5 cm2. Note: The key concept for solving this problem is the segregation of the whole area into two parts. By separating the area into rectangle and triangle be easily evaluated as the area of the whole polygon.
Which figure is a polygon?
A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides.
How do you find the area of a polygon with coordinates?
By finding the product of a point’s x coordinate times the next point’s y coordinate, then subtracting the y coordinate of the first point times the x coordinate of the second coordinate and dividing by two, you will find the area of the polygon.
What is apothem in polygon?
The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. The word “apothem” can also refer to the length of that line segment.
What is the area of a polygon with 4 sides?
1 × Diag. 2)/2 or A = (d1 × d2)/2. Example: A four-sided shape has two adjacent sides with lengths of 4 meters. You can find the area of this square by multiplying its base times its height: 4 × 4 = 16 square meters.
What is a polygon Class 6?
A polygon is a closed figure formed of three or more line segments. Examples of polygons are triangle, quadrilateral, pentagon and. hexagon.
What is a polygon class 8?
A polygon is a simple closed curve made up of line segments only. Polygons are classified according to the number of sides they have. What are Adjacent Sides? If the two sides of a polygon have a common vertex then they are called the adjacent sides of the polygon.
What is diagonal polygon?
A diagonal is a segment of a polygon that connects two non-consecutive vertices. … A diagonal of a polygon can be defined as a line segment joining two vertices. From any given vertex, there are no diagonals to the vertex on either side of it, since that would lay on top of the side.
How do you find area?
Area is calculated by multiplying the length of a shape by its width.
How many polygons are there?
Name of the Polygons | Sides | Vertices |
---|---|---|
Quadrilateral (also called Tetragon) | 4 | 4 |
Pentagon | 5 | 5 |
Hexagon | 6 | 6 |
Heptagon | 7 | 7 |
How do you find the area of a pentagon with coordinates?
Area of a polygon given its coordinates:
Given the coordinates of a polygon with n-sides, this formula to solve the area of any polygon is given by, Area=12|(x1y2−y1x2)+((x2y3−y2x3)….
How do you find the area of a regular polygon with only the side lengths?
You also learned the formula for finding the area of any regular polygon if you know the length of one side and the apothem: A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothem.
How do you find the radius of a polygon?
The radius of a regular polygon is the distance from the center to any vertex. It will be the same for any vertex. The radius is also the radius of the polygon’s circumcircle, which is the circle that passes through every vertex.
How do you find the center of a polygon?
Compute the centre position (x,y) of each edge of the polygon. You can do this by finding the difference between the positions of the ends of each edge. Take the average of each centre in each dimension. This will be the centre of the polygon.
What is the formula for finding the area of a regular polygon with perimeter P and apothem length A?
The area of a regular polygon will be ½ (a × p), where a is the apothem and p is the perimeter. The perimeter of a regular polygon is just the number of sides, times the length of each side.
How do you find the area of different sides?
- Step 1: Measure all sides of the area in one unit (Feet, Meter, Inches or any other).
- Step 2: Enter length of horizontal sides into Length 1 and Length 2. And Width of the vertical sides into Width 1 and Width 2. …
- Step 3: Press calculate button. …
- Our Formula: Area = b × h.
What is a polygon answer?
Answer: A polygon refers to any two-dimensional shape whose formation takes place with straight lines. Triangles, hexagons, pentagons, and quadrilaterals are all examples of polygons. … For example, a triangle consists of three sides while a quadrilateral consists of four sides.
What are diagonal in math?
In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. … In matrix algebra, a diagonal of a square matrix is a set of entries extending from one corner to the farthest corner. There are also other, non-mathematical uses.
What is polygon in statistics?
A frequency polygon is a graph constructed by using lines to join the midpoints of each interval, or bin. … The heights of the points represent the frequencies. A frequency polygon can be created from the histogram or by calculating the midpoints of the bins from the frequency distribution table.
What is regular polygon in maths?
A polygon is called regular if it has equal sides and angles. Thus, a regular triangle is an equilateral triangle, and a regular quadrilateral is a square.
What is polygon BYJU’s?
A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.
Is a square a polygon?
Non-Euclidean geometry
In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle. Larger spherical squares have larger angles.