1. What are 2D Shapes?
2D Shapes are two-dimensional flat shapes that have length and width but no height. Some common 2D shapes are quadrilaterals like squares and rectangles, polygons, and circles.
1.1 2D Shapes: Quadrilaterals
Quadrilaterals are 2D shapes with four sides and four angles. The Sum of all four angles of quadrilaterals is 360 degrees. For 11 plus exams, you must know the following six types of quadrilaterals and their properties:
a) Square
- Four right angles
- Four equal sides
- Opposite sides are parallel
b) Rectangle
- Four right angles
- Opposite sides are of equal length
- Opposite sides are parallel
c) Parallelogram
- Opposite sides are of equal length
- Opposite sides are parallel
- Diagonally opposite angles are equal
d) Rhombus
- Four equal sides
- Opposite sides are parallel
- Diagonally opposite angles are equal
e) Kite
- Two pairs of equal sides
- One pair of opposite angles are equal
f) Trapezium
- Has exactly one pair of parallel side
1.2 Solved Example
Ruby put five shapes into a box. She pulled one out at random. The shape had exactly one pair of parallel sides, no equal sides, and two obtuse angles.
Which of the following shapes did Ruby pull out of the box?
Solution:
Option A has two pairs of parallel sides.
Option B has two pairs of equal sides.
Option C has one pair of parallel sides, no equal sides, and two obtuse angles.
Option D has no parallel sides.
Option E has two pairs of parallel sides.
Option C matches the description of the shape that Ruby chose.
Option C is correct.
2. Polygons
The term ‘poly’ means many and ‘gons’ means sides. Polygons are 2D shapes with three or more sides. Polygons with 3 sides are triangles, four sides are quadrilaterals.
Polygons are classified as regular and irregular polygons.
2.1 Regular polygons and examples
Polygons with all sides and angles of the same measure are called regular polygons. Below are some examples and properties of regular polygons.
a) Equilateral Triangle
- Polygon with three equal sides.
- Three equal angles
b) Regular Pentagon
- Polygon with five equal sides
- Five equal angles
c) Regular Octagon
- Polygon with eight equal sides
- Eight equal angles
2.2 Irregular polygons and examples
Polygons with at least one side or angle that is different in size are called irregular polygons.
a) Irregular Hexagon
b) Irregular Pentagon
3. Circles
A circle is a round 2D shape formed by a curved line. Any point on this line is always the same distance from the centre. This distance is called the radius of the circle. It has no sides and corners.
The distance OA is the radius of the above circle.
Any line passing through the centre of the circle touching the curved line of the circle is called the diameter of the circle. The diameter of the circle is twice its radius.
The distance AB is the diameter of the above circle and AB is twice the radius OA or OB.
3.1 Solved Example
Work out the radius of the circle whose diameter is 50 cm.
Solution:
Given the diameter of the circle d =50 cm
Let the radius of the circle be r.
Diameter is twice the radius.
d=2×r
r=d÷2
r=50÷2
r=25 cm
Radius of the circle is 25 cm.
