Exterior angle
Number of sides
Test Your Understanding:
a.
A regular polygon has an exterior angle of
. How many sides does it have?
b.
A regular polygon has an interior angle of
. How many sides does it have?
c.
A regular polygon has 15 sides. What is each interior angle?

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d.
The diagram on the left shows a regular hexagon and a
regular octagon. Calculate the angle
119. Use geometric language
appropriately and recognise
and name pentagons,
hexagons, heptagons, octagons
and decagons
Simply a case of memorisation.
Num sides
Name
Num sides
Name
4
Quadrilateral
8
Octagon
5
Pentagon
9
Nonagon
6
Hexagon
10
Decagon
7
Heptagon (not ‘septagon’!)
120. Understand tessellations
of regular and irregular
polygons and combinations of
polygons. Explain why some
shapes tessellate when other
shapes do not.
.
Shapes tessellate (whether multiple copies of the same shape or
different shapes) when the interior angles joining at a point sum
to
. For example, a hexagon tessellates with itself as we can
join 3 hexagons each with interior angle
, whereas a
pentagon does not tessellate because its interior angle of
is
not a factor of 360.
More complicated problems might require to you to find the
interior angle first before calculating the number of sides
e.g. “
Two copies of a regular polygon
and a square tessellate as pictured. Prove
that
is an octagon.”
At any point in the diagram, there is one square and two copies of
. Thus interior
angle of
is
.
Exterior angle of
Number of sides of
, thus
is an octagon.
Test Your Understanding:
A pattern is made up of two tiles, A and B,
as pictured on the right. Both tiles are regular polygons. Work out
how many sides Tile A has.
2D and 3D Shapes
121. Use 2-D representations of
3-D shapes. Use isometric grids.
Draw nets and show how they
fold to make a 3-D solid
An isometric grid is one which consists of equilateral triangles, inside of the usual squares.
122. Understand and draw
front and side elevations and
plans of shapes made from
simple solids. Given the front
and side elevations and the
plan of a solid, draw a sketch of
the 3-D solid
Recall that the plan is the view from the top, the front elevation is the horizontal view from
the designated ‘front’ (which will be indicated), and the
side elevation the horizontal view
from the side.
Example:
Consider the following shapes sketched isometrically:
Then the plan, front elevation and side
elevation are as follows. Ensure you correctly
count the number of squares!
Test Your Understanding:
A cuboid is
as pictured. On a square grid, draw
the plan, front elevation and side elevation.

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