What you need to know
A polygon is a many sided shape made up of straight edges.
There are two types of polygons you need to know about:
- Regular– All sides and angles the same length
- Irregular– All sides and angles are not the same length
You will already be familiar with the names of some shapes, but it’s important to recognise the names of shapes that have up to 10-sides, as seen below.
All of these shapes are regular polygons, meaning that all of their sides are thesame length and all the angles are the same.
Look at the the irregular shapes shown:
Shape A – Counting the number of sides, we see that shape A has 4 sides, therefore it is a quadrilateral.
(Squares are special quadrilateral but still quadrilaterals)
Shape B – Doing the same for B, we see that it has 7 sides, and therefore it is a heptagon.
Quadrilaterals : 6 Common Types
Triangles and quadrilaterals are the shapes we will see most often. As a result, we have names for specific types of them.
The different types of quadrilaterals you should be familiar with are:
1. Square – Has 4 sides equal in length, and 4 equal angles.
2. Rectangle – Has 4 equal angles (all 90\degree), and its opposite sides are equal in length.
3. Trapezium – Has one pair of parallel sides.
4. Kite – Has two pairs of equal sides, and each pair must be adjacent to each other. Additionally, two of its angles (as marked on the picture) are equal.
5. Parallelogram – Has two pairs of parallel sides. Additionally, opposite angles are equal and adjacent angles add to 180\degree.
6. Rhombus – Has 4 sides equal in length. Additionally, opposite angles are equal, and opposite sides are parallel.
The different types of triangles you should be familiar with are:
1. Equilateral – Has 3 sides equal in length, and all 3 angles are 60\degree
2. Isosceles – Has 2 sides equal in length, and the two base angles are equal.
3. Right-angled – Has 1 angle equal to 90\degree.
4. Scalene – Has 3 sides of different lengths, and no angles are the same.
Firstly, realising that C has 5 triangular faces immediately rules it out, since a square-based pyramid only has 4. That leaves A and B. If you try and fold along the edges of B, using the square face as your base, you will find that two of the triangles overlap and there is a gap, so this does not work.
Therefore, A must be the correct net, and indeed if we try to fold it, we will find this to be the case.
Worksheets and Exam Questions
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