Apr 28, It might help to know the definition of a polygon. Explanation: A polygon is a 2-dimensional, many-sided closed figure. Related questions How do you classify the triangle given 2 cm, 2 cm, 2 cm? The angles of a triangle have the ratio What is the measure of the smallest angle? Is an equilateral triangle is sometimes, never or always an isosceles triangle? What is an isosceles triangle? How do I prove that these are the vertices of an isosceles triangle: -3,0 , 0,4 , 3,0?
The angles between the sides of shapes are important when defining and working with polygons. See our page on Angles for more about how to measure angles. There is a useful formula for finding out the total or sum of internal angles for any polygon, that is:. Furthermore, if the shape is a regular polygon all angles and length of sides are equal then you can simply divide the sum of the internal angles by the number of sides to find each internal angle. As well as the number of sides and the angles between sides, the length of each side of shapes is also important.
If your shape is a regular polygon such as a square in the example above then it is only necessary to measure one side as, by definition, the other sides of a regular polygon are the same length. It is common to use tick marks to show that all sides are an equal length. In the example of the rectangle we needed to measure two sides - the two unmeasured sides are equal to the two measured sides. It is common for some dimensions not to be shown for more complex shapes. In such cases missing dimensions can be calculated.
The missing horizontal length can be calculated. Take the shorter horizontal known length from the longer horizontal known length. The simplest and most basic polygon for the purposes of calculating area is the quadrilateral. To obtain the area, you simply multiple length by vertical height. For parallelograms, note that vertical height is NOT the length of the sloping side, but the vertical distance between the two horizontal lines. This is because a parallelogram is essentially a rectangle with a triangle cut off one end and pasted onto the other:.
You can see that if you remove the left-hand blue triangle, and stick it onto the other end, the rectangle becomes a parallelogram. The area is length the top horizontal line multiplied by height, the vertical distance between the two horizontal lines. To work out the area of a triangle , you multiple length by vertical height that is, the vertical height from the bottom line to the top point , and halve it.
This is essentially because a triangle is half a rectangle. To calculate the area of any regular polygon , the easiest way is to divide it into triangles, and use the formula for the area of a triangle. See our page Calculating Area for more, including examples.
See our Introduction to Trigonometry page for more information. An obtuse triangle will always have one angle whose measure is greater than 90 degrees but at the same time less than degrees.
A median of a triangle is a segment drawn from a vertex of the triangle to the midpoint of the opposite side. An altitude or height of a triangle is a segment drawn from a vertex of the triangle perpendicular to the opposite side or to the opposite side extended.
The word distance in geometry is always understood as the shortest path. The distance between a point and a line is the length of the perpendicular segment drawn from a point that is not on the line to a point on the line. The distance from A to line BC below is 6, because that is the length of the altitude. Definition A polygon is a closed geometric figure whose sides are simple line segments. Classification of Polygons A polygon may be identified by the number of sides. A polygon of 8 sides is called an octagon.
A polygon of 10 sides is called a decagon. A polygon of 12 sides is called a dodecagon.
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