Polygons
ICSE Class 6 · Mathematics · Chapter 28
What this chapter covers
- What is a polygon?
- Naming polygons by the number of sides
- Regular and irregular polygons
- Diagonals of a polygon
Key points
- A polygon is a closed figure made of three or more line segments that meet only at their end points and never cross each other.
- A closed figure whose segments cross, such as a bow-tie, is not a polygon.
- A polygon has the same number of sides, vertices and angles.
- Polygons are named by their number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7) and octagon (8).
- A regular polygon has all sides equal and all angles equal; any other polygon is irregular.
- A square is a regular quadrilateral; a rhombus or rectangle that is not a square is irregular.
- A regular hexagon can be drawn by stepping the radius of a circle six times round it.
- The perimeter of a regular polygon is the length of one side multiplied by the number of sides.
- A diagonal joins two vertices that are not adjacent; a triangle has none.
- To count diagonals, find how many start at one vertex, multiply by the number of vertices, then halve.
Questions answered
Is a circle a polygon? Give a reason.
No. A circle is curved, and a polygon is made only of straight line segments.
A polygon has 7 vertices. How many sides and angles does it have, and what is it called?
It has 7 sides and 7 angles. It is a heptagon.
Name the polygon with five sides and the polygon with eight sides.
A pentagon has five sides. An octagon has eight sides.
Give one example of a hexagon from everyday life.
A cell of a honeycomb, or the head of a nut or bolt.
A rhombus has all four sides equal. Is every rhombus a regular polygon? Explain.
No. A regular polygon needs equal angles as well. A rhombus usually has unequal angles, so it is regular only when it is a square.
In pentagon VWXYZ, is VX a side or a diagonal?
VX is a diagonal, because V and X are not adjacent vertices.
How many diagonals does a heptagon have?
From each vertex, 7 - 3 = 4 diagonals start. Then 7 × 4 = 28, and 28 ÷ 2 = 14. A heptagon has 14 diagonals.
A regular pentagon has a side of 6 cm. Find its perimeter.
Perimeter = 5 × 6 = 30 cm.