Topicmf0af8850faac5179_1528449000663_0Topic

The area of the trapezium

Levelmf0af8850faac5179_1528449084556_0Level

Second

Core curriculummf0af8850faac5179_1528449076687_0Core curriculum

Student:

2) uses the formulas to calculate the area of the triangle, the rectangle, the square, the parallelogram, the rhombus and the trapezoid; is able to determine the lengths of line segments in tasks of comparable difficulty:

a) calculate the shortest altitude of the right triangle whose sides are: 5 cm, 12 cm and 13 cm;

b) The diagonals of the rhombus ABCD are AC = 8 dm i BD = 10 dm. The diagonal BD is extended to point E in such a way that the line segment BE is twice as long as this diagonal. Calculate the area of the triangle CDE. (There are two possible answers)

Timingmf0af8850faac5179_1528449068082_0Timing

45 minutes

General objectivemf0af8850faac5179_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmf0af8850faac5179_1528449552113_0Specific objectives

1. Calculating the area of the trapezium

2. Calculating the lengths of the sides of the trapezium of the given area.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesmf0af8850faac5179_1528450430307_0Learning outcomes

Student:

1. calculates the area of the trapezium,

2. calculates the lengths of the sides of the trapezium of the given area.

Methodsmf0af8850faac5179_1528449534267_0Methods

1. Discussion.

2. Brainstorming.

Forms of workmf0af8850faac5179_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmf0af8850faac5179_1528450127855_0Introduction

The teacher informs the students that during this class they will learn the formulaformulaformula for the area of the trapeziumthe area of the trapeziumthe area of the trapezium. They will calculate the area of the right‑angled trapeziumthe right‑angled trapeziumthe right‑angled trapezium and the isosceles trapeziumisosceles trapeziumisosceles trapezium. They will also determine the lengths of the sides of the trapezium of the given area.

Task:

Students revise the properties of the right‑angled trapeziumthe right‑angled trapeziumthe right‑angled trapezium and the isosceles trapeziumisosceles trapeziumisosceles trapezium.

Proceduremf0af8850faac5179_1528446435040_0Procedure

[Geogebra applet]

Students work individually using computers. Their task is to determine the formulaformulaformula for the area of the trapeziumthe area of the trapeziumthe area of the trapezium.

Having completed the exercise, students together think if there is some other way to determine the area of the trapeziumthe area of the trapeziumthe area of the trapezium (for example, by dividing it into triangles). They make hypotheses and check them. At the end of the exercise they should formulate the formulaformulaformula for the area of the trapeziumthe area of the trapeziumthe area of the trapezium:

The area of the trapeziumthe area of the trapeziumThe area of the trapezium equals the product of half of the sum of its bases and its altitude.

Conclusion:

The area of the trapeziumthe area of the trapeziumThe area of the trapezium whose bases are a and b and whose altitude is h, is expressed with the following formulaformulaformula:

[illustration 1]

$P=\frac{a+b}{2}\cdot h$

Students use the derived formulaformulaformula in the following exercises:

Task:

The area of the trapeziumthe area of the trapeziumThe area of the trapezium is 20. Calculate the length of the x side.

[illustration 2]

Task:

Calculate the area of the isosceles trapeziumisosceles trapeziumisosceles trapezium, whose perimeter is 22 cm. One of its bases is 4 cm and the other is two times longer. The altitude of the trapeziumthe altitude of the trapeziumThe altitude of the trapezium is 2 cm shorter than the leg.

Task:

Calculate the area of the trapeziumthe area of the trapeziumthe area of the trapezium whose bases are 4 cm and 8 cm and the angles at the longer base are 30° and 60°.

[Illustration 3]

An extra task:

Students calculate the area of the regular hexagon whose side is 4 dm.

Lesson summarymf0af8850faac5179_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

The area of the trapeziumthe area of the trapeziumThe area of the trapezium: $P=\frac{a+b}{2}\cdot h$.

Selected words and expressions used in the lesson plan

formulaformulaformula

isosceles trapeziumisosceles trapeziumisosceles trapezium

the altitude of the trapeziumthe altitude of the trapeziumthe altitude of the trapezium

the area of the trapeziumthe area of the trapeziumthe area of the trapezium

the perimeter of the trapeziumthe perimeter of the trapeziumthe perimeter of the trapezium

the right‑angled trapeziumthe right‑angled trapeziumthe right‑angled trapezium