What is the difference between concave and convex polygons

Convex and concave shapes are different. The table below shows the differences between convex and concave polygon. A polygon is a shape that has a minimum of three sides and three angles. Every shape occupies some amount of space.

This is called an area. The formulas given below helps to easily find the area , sum of the exterior angles, and sum of the interior angles of a convex polygon. The space covered inside the boundary of a convex polygon is its area.

For example, a hexagon has 6 sides. Example 1: What is the measure of an interior angle of a regular convex polygon like a pentagon?

Hence, the sum of the interior angles of the pentagon is:. Among the given shapes, a , d , and f have all their vertices pointing outwards. Therefore, these are the only convex polygon among the given shapes. Therefore, a , d and f are convex polygons. Example 3: Find the area of a regular convex polygon whose vertices are 6,8 , 4. A convex polygon is a shape in which all of its sides are pointing or protruding outwards.

An isosceles right triangle has legs that are each 4cm. What is the length of the hypotenuse? Triangle XYZ is isosceles. The base angles, angle X and angle Y, are four times the measure of What is the isosceles triangle theorem? In congruent polygons, every segment is congruent. SparkTeach Teacher's Handbook. Summary Different Kinds of Polygons.

Convex and Concave Polygons Every polygon is either convex or concave. Previous section Problems Next section Problems. A convex polygon is the one in which none of the angles point inwards. In other words, it has no internal angle that is greater than degrees. A polygon with any of the internal angles greater than degrees is known as a concave polygon. In other words, a concave polygon exists with an interior reflex angle. A simple line test can be used to distinguish a concave polygon with a convex polygon.

If a line is drawn that passes through the polygon, and it always passes through only two of the lines or polygons making up the shape, then in that case, the shape of the polygon is convex. On the other hand, if the same process is repeated in a concave shape, then the line is able to pass through more than two of the lines. In 3 dimensional shapes, the same test can be performed to differentiate between the two.

It is important to note that all the diagonals of a convex polygon lie entirely inside the polygon.