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Other polygons

There are many other polygons, some of which are given in the table below.

Table 1: Table of some polygons and their number of sides.
Sides Name
5 pentagon
6 hexagon
7 heptagon
8 octagon
10 decagon
15 pentadecagon
Figure 1: Examples of other polygons.
Figure 1 (MG10C13_046.png)

Extra

Angles of Regular Polygons

You can calculate the size of the interior angle of a regular polygon by using:

A ^ = n - 2 n × 180 ∘ A ^ = n - 2 n × 180 ∘
(1)

where nn is the number of sides and A^A^ is any angle.

Areas of Polygons

  1. Area of triangle: 12×12× base ×× perpendicular height
    Figure 2
    Figure 2 (MG10C13_047.png)
  2. Area of trapezium: 12×12× (sum of ∥∥ (parallel) sides) ×× perpendicular height
    Figure 3
    Figure 3 (MG10C13_048.png)
  3. Area of parallelogram and rhombus: base ×× perpendicular height
    Figure 4
    Figure 4 (MG10C13_049.png)
  4. Area of rectangle: length ×× breadth
    Figure 5
    Figure 5 (MG10C13_050.png)
  5. Area of square: length of side ×× length of side
    Figure 6
    Figure 6 (MG10C13_051.png)
  6. Area of circle: ππ x radius22
    Figure 7
    Figure 7 (MG10C13_052.png)

Figure 8
Khan Academy video on area and perimeter

Figure 9
Khan Academy video on area of a circle

Polygons

  1. For each case below, say whether the statement is true or false. For false statements, give a counter-example to prove it:
    1. All squares are rectangles
    2. All rectangles are squares
    3. All pentagons are similar
    4. All equilateral triangles are similar
    5. All pentagons are congruent
    6. All equilateral triangles are congruent
    Click here for the solution
  2. Find the areas of each of the given figures - remember area is measured in square units (cm22, m22, mm22).
    Figure 10
    Figure 10 (MG10C13_053.png)
    Click here for the solution

Summary

  • Make sure you know what: quadrilaterals, vertices, sides, angles, parallel lines, perpendicular lines,diagonals, bisectors and transversals mean.
  • Similarities and differences between quadrilaterals
  • Properties of triangles and quadrilaterals
  • Congruency of triangles
  • Classification of angles into acute, right, obtuse, straight, reflex or revolution
  • Theorem of Pythagoras which is used to calculate the lengths of sides of a right-angled triangle
  • Angles:
    • Acute angle: An angle 0 and 90
    • Right angle: An angle measuring 90
    • Obtuse angle: An angle 90 and 180
    • Straight angle: An angle measuring 180◦
    • Reflex angle: An angle 180 and 360
    • Revolution: An angle measuring 360
  • Angle properties and names
  • Equilateral, isoceles, right-angled, scalene triangles
  • Triangles angles = 180
  • Congruent and similar triangles
  • Pythagoras
  • Trapezium, parm, rectangle, square, rhombus, kite and properties
  • Areas of particular figures

Exercises

  1. Find all the pairs of parallel lines in the following figures, giving reasons in each case.
    1. Figure 11
      Figure 11 (MG10C13_054.png)
    2. Figure 12
      Figure 12 (MG10C13_055.png)
    3. Figure 13
      Figure 13 (MG10C13_056.png)
    Click here for the solution
  2. Find angles aa, bb, cc and dd in each case, giving reasons.
    1. Figure 14
      Figure 14 (MG10C13_057.png)
    2. Figure 15
      Figure 15 (MG10C13_058.png)
    3. Figure 16
      Figure 16 (MG10C13_059.png)
    Click here for the solution
  3. Which of the following claims are true? Give a counter-example for those that are incorrect.
    1. All equilateral triangles are similar.
    2. All regular quadrilaterals are similar.
    3. In any ▵ABC▵ABC
      with ∠ABC=90∘∠ABC=90∘ we have AB3+BC3=CA3AB3+BC3=CA3.
    4. All right-angled isosceles triangles with perimeter 10 cm are congruent.
    5. All rectangles with the same area are similar.
    Click here for the solution
  4. Say which of the following pairs of triangles are congruent with reasons.
    1. Figure 17
      Figure 17 (MG10C13_060.png)
    2. Figure 18
      Figure 18 (MG10C13_061.png)
    3. Figure 19
      Figure 19 (MG10C13_062.png)
    4. Figure 20
      Figure 20 (MG10C13_063.png)
    Click here for the solution
  5. For each pair of figures state whether they are similar or not. Give reasons.
    Figure 21
    Figure 21 (MG10C13_064.png)
    Click here for the solution

Challenge Problem

  1. Using the figure below, show that the sum of the three angles in a triangle is 180∘∘. Line DEDE
    is parallel to BCBC.
    Figure 22
    Figure 22 (MG10C13_065.png)

    Click here for the solution

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