GoalDecide whether a shape is a polygon and find the perimeter of a polygon.
New words
polygon · a closed flat shape with only straight sidesclosed · with no gap, so the sides meet all the way roundvertex · a corner where two sides meetregular polygon · a polygon with all sides equal and all angles equal
Explanation
A polygon is a flat shape that is closed and has only straight sides. Closed means there is no gap, so the sides meet all the way round. A circle is not a polygon, because its edge is curved. A shape with a gap is not a polygon either. A polygon is named by its number of sides: a triangle has 3, a quadrilateral 4, a pentagon 5, a hexagon 6 and an octagon 8. To find the perimeter of any polygon, add the lengths of all its sides. If all the sides are equal we can multiply. A hexagon with 6 sides of 4 cm has a perimeter of 6 × 4 = 24 cm.
Worked examples
Which shapes are polygons? A is a triangle and C is a hexagon: both closed with straight sides. B is a circle and D is an oval: their edges are curved. So A and C are polygons.
This shape has straight lines, but there is a gap on the left side. It is not closed, so it is not a polygon.
This regular pentagon has 5 equal sides of 3 cm. The perimeter is 5 × 3 = 15 cm. We can also add 3 + 3 + 3 + 3 + 3 = 15 cm.
Class activity
Polygon hunt. Walk around your home or street and find a polygon with 3 sides, one with 4 sides and one with more sides, for example a road sign or a window. Draw each one and write its name. Then find something with a curved edge that is not a polygon.
Practice
1
Which shapes are polygons?
A and C, the rectangle and the pentagon. B is an oval and D is a circle, so their edges are curved.
2
Is this shape a polygon? Why?
No. The lines do not make a closed shape, because the two ends are not joined.
3
A regular hexagon has 6 sides of 5 cm each. What is its perimeter?
6 × 5 = 30 cm.
4
An octagon has 8 equal sides of 3 cm. What is its perimeter?
8 × 3 = 24 cm.
5
A pentagon has sides of 4 cm, 5 cm, 6 cm, 3 cm and 7 cm. What is its perimeter?
