2D Shapes

2D Shapes

Your child needs to be familiar with 2D shapes for their exam. A 2D shape is a flat area, you can think of it as a sheet of paper. They have length and width but no depth.

Quadrilaterals

A quadrilateral shape is a 2D shape that has four sides.

The notation of arrows on the sides of the shapes means that those two sides are parallel.

Some examples of quadrilateral shapes are:

Square:

  • 4 equal sides
  • 4 right angles (90\degree)
  • 2 pairs of parallel sides

 

Rectangle:

  • 2 pairs of equal sides
  • 4 right angles (90\degree)
  • 2 pairs of parallel sides

 

 

Trapezium:

  • 1 pair of parallel sides

Rhombus: 

  • 4 equal sides
  • 2 equal acute angles (less than 90\degree)
  • 2 equal obtuse angles (greater than 90\degree)
  • 2 pairs of parallel sides

Parallelogram:

  • 2 pairs of equal sides
  • 2 equal acute angles (less than 90\degree)
  • 2 equal obtuse angles (greater than 90\degree)
  • 2 pairs of parallel sides

 

 

Kite: 

  • 2 pairs of equal sides
  • 2 equal angles

Triangles

Triangles are shapes with three sides and three angles.

There are \bold{\textcolor{darkturquoise}{4}} different types of triangle that have different properties.

Equilateral Triangle: 

  • 3 equal angles
  • 3 equal sides

 

 

Isosceles Triangle:

  • 2 equal angles
  • 2 equal sides

 

 

Right-Angled Triangle:

  • 1 right angle

Right-angled triangles can also be scalene or isosceles and have other properties but they just have to have 1 right angle to class as a right-angled triangle.

 

Scalene Triangle:

  • No equal sides
  • No equal angles

Circles

A circle just has one side and no corners.

  • The circumference is the length of the outside of the circle.
  • The diameter is the length from one side of the circle to the opposite side. The diameter must pass through the centre of the circle.
  • The radius is half of the length of the diameter. This is an important fact for your child to remember as they may be asked a question about it in their exam.

Other Polygons

So, far we have only looked at 2D shapes with 4 or less sides.

But your child should be aware of other shapes that have more than 4 sides and be able to identify them.

A polygon is a word used to describe these 2D shapes. A polygon is regular when all of the sides and angles are the same size.

For example, a square is a regular quadrilateral as it has 4 equal sides and 4 equal angles.

  • A regular pentagon has \bold{\textcolor{blue}{5}} equal sides and \bold{\textcolor{blue}{5}} equal angles.
  • A regular hexagon has \bold{\textcolor{purple}{6}} equal sides and \bold{\textcolor{purple}{6}} equal angles.
  • A regular heptagon has \bold{\textcolor{orange}{7}} equal sides and \bold{\textcolor{orange}{7}} equal angles.
  • A regular octagon has \bold{\textcolor{green}{8}} equal sides and \bold{\textcolor{green}{8}} equal angles.

2D Shapes Example Questions

Question 1: Which of the following shapes have 2 pairs of parallel sides?

[1 mark]

Shape A is a trapezium. So, it has only 1 pair of parallel sides.

Shape B is  triangle and shape E is a circle. Both of these shapes have no pairs of parallel sides.

Shape C is a rectangle so does have 2 pairs of parallel sides.

Similarly, shape D is a parallelogram so also has 2 pairs of parallel sides.

So, the answer is shape C and shape D

Question 2: Name the following shapes from a description of their properties.

a) This shape has 4 equal sides and 2 pairs of equal angles.

b) This shape has 3 sides, 2 of which are equal and 2 equal angles.

[2 marks]

a) As this shape has 4 equal sides we can narrow down the possibilities to a square or a rhombus. A square has 4 equal right angles but our shape has 2 pairs of equal angles so it must be a rhombus.

b) Our shape has 3 sides this time which tells us that the shape is a triangle.

Which type of triangle has 2 equal sides and 2 equal angles?

Isosceles triangle

Question 3: A circle has a diameter of 750\text{ m}.

What is the radius of the circle?

[1 mark]

Your child should be able to recall that the diameter of a circle is double its radius.

Therefore, to find the radius from the diameter, we need to halve it or divide it by \bold{\textcolor{darkturquoise}{2}}.

750\text{ m} \textcolor{darkturquoise}{\div 2} = 375\text{ m}

So, the radius of this circle is 375\text{ m}