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:

  • 44 equal sides
  • 44 right angles (90°)(90degree)
  • 22 pairs of parallel sides

 

Rectangle:

  • 22 pairs of equal sides
  • 44 right angles (90°)(90degree)
  • 22 pairs of parallel sides

 

 

Trapezium:

  • 11 pair of parallel sides

Rhombus: 

  • 44 equal sides
  • 22 equal acute angles (less than 90°90degree)
  • 22 equal obtuse angles (greater than 90°90degree)
  • 22 pairs of parallel sides

Parallelogram:

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

 

 

Kite: 

  • 22 pairs of equal sides
  • 22 equal angles
11 Plus Essentials Pack

Triangles

Triangles are shapes with three sides and three angles.

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

Equilateral Triangle: 

  • 33 equal angles
  • 33 equal sides

 

 

Isosceles Triangle:

  • 22 equal angles
  • 22 equal sides

 

 

Right-Angled Triangle:

  • 11 right angle

Right-angled triangles can also be scalene or isosceles and have other properties but they just have to have 11 right angle to class as a right-angled triangle.

 

Scalene Triangle:

  • No equal sides
  • No equal angles
11 Plus Essentials Pack

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 44 or less sides.

But your child should be aware of other shapes that have more than 44 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 44 equal sides and 44 equal angles.

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

2D Shapes Example Questions

Question 1: Which of the following shapes have 22 pairs of parallel sides?

[1 mark]

Shape A is a trapezium. So, it has only 11 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 22 pairs of parallel sides.

Similarly, shape D is a parallelogram so also has 22 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 44 equal sides and 22 pairs of equal angles.

b) This shape has 33 sides, 22 of which are equal and 22 equal angles.

[2 marks]

a) As this shape has 44 equal sides we can narrow down the possibilities to a square or a rhombus. A square has 44 equal right angles but our shape has 22 pairs of equal angles so it must be a rhombus.

b) Our shape has 33 sides this time which tells us that the shape is a triangle.

Which type of triangle has 22 equal sides and 22 equal angles?

Isosceles triangle

Question 3: A circle has a diameter of 750 m750text{ 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 2bold{textcolor{darkturquoise}{2}}.

750 m÷2=375 m750text{ m} textcolor{darkturquoise}{div 2} = 375text{ m}

So, the radius of this circle is 375 m375text{ m}