Topic 10: Length and Area Properties of Two-dimensional Geometrical Figures

By the end of this topic, you will be able to:

(a) describe the length of two- dimensional geometrical figures.

(b) develop, understand and state Pythagoras’ theorem.

(c) apply Pythagoras’ theorem to right-angled and isosceles triangles.

(d) understand the meaning of area in two-dimensional geometrical figures (triangles, rectangles).

Keywords

• hypotenuse length
• perimeter
• Pythagoras’ theorem
• right-angled
• two-dimensional
• geometrical figures
• width
• length

Introduction

In primary school, you studied about lines and areas of shapes like triangles, rectangles, square, circle, trapezium and others. In this topic, you will use the same knowledge to understand, justify and apply area and perimeter formulae for such different length and figures.

10.1 Describing two-dimensional geometrical figures

Activity 10.1 Identifying the properties of two-dimensional geometrical figures.

Study the figures below and use them to fill in the table provided.

1. Copy and complete the table below.

2. Draw and describe at least three other figures other than those named above which you think are two-dimensional.

Activity 10.2 Making models of two-dimensional geometrical figures

1. Cut out from manilla paper different types of two-dimensional geometrical figures. Name each of them and indicate the number of sides for each of the figures.
2. Explain why the figures you have made are called two- dimensional figures.
3. Share your work with the class.

Exercise 10.1

From the list below, identify and draw figure which are two-dimensional.

1. Triangle

2. Line

3. Cube

4. Square

5. Parallelogram

6. Trapezium

7. Rectangle

8. Cuboid

9. Kite

10. Pyramid

11. Circle

12. Box

13. Kite

14. Rhombus

10.2 Developing and stating Pythagoras’ theorem

You have previously used Pythagoras’ theorem in primary school. In this section, you will develop the theorem and then apply it to solve problems.

Activity 10.3 Generating the Pythogoras’ theorem

1. Draw triangle ABC on squared paper or graph paper such that one of the angles is 90°.
2. Construct squares on the three sides of the triangle and establish the connection among the areas of these three squares. Hence state Pythagoras’ theorem using the sides of the triangle.
3. Share your work with the rest of the class members.

Learning point

Pythagoras’ theorem applies only to a right-angled triangle

10.3 Applying Pythagoras’ theorem to right-angled triangle and isosceles triangle

Activity 10.4 Using Pythagoras’ theorem

1. Carefully study the shape of the floor of your classroom.
2. Establish the length of the diagonal of your classroom without measuring it directly.
3. Share your findings with the rest of the class.

Exercise 10.3 1.

For each of the right-angled triangles, calculate the length of the side marked with a letter.

10.4 Undestanding the meaning of area of two- dimensional figures

Activity 10.5 Finding the area of two-dimensional figures 2.

1. Plot a rectangle ABCD whose vertices are at (2,1), (6,1), (6,7) and (2,7) respectively. Count the squares to establish the area of: (a) rectangle ABCD. (b) triangle ABC. (c) triangle ADC.
2. Other than counting squares, how else can you obtain the area for each of the three named figures in (1)?

Exercise 10.4

1. Find the area of the following figures.

Given that AH = DF = 2 cm, find the area of the shaded region.

3. In the figure below, AB is parallel to DC. With the dimensions indicated, find the area of quadrilateral ABCD.