Topicmaac083a7c0d6e162_1528449000663_0Topic

The area of the trianglearea of the trianglearea of the triangle

Levelmaac083a7c0d6e162_1528449084556_0Level

Second

Core curriculummaac083a7c0d6e162_1528449076687_0Core curriculum

IX. Polygons. The student:

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

a) calculate the shortest altitudealtitudealtitude 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 trianglearea of the trianglearea of the triangle CDE (there are two possible answers).

Timingmaac083a7c0d6e162_1528449068082_0Timing

45 minutes

General objectivemaac083a7c0d6e162_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmaac083a7c0d6e162_1528449552113_0Specific objectives

1. Calculating the area of the trianglearea of the trianglearea of the triangle.

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

Learning outcomesmaac083a7c0d6e162_1528450430307_0Learning outcomes

The studwent calculates the area of the trianglearea of the trianglearea of the triangle.

Methodsmaac083a7c0d6e162_1528449534267_0Methods

1. Discussion.

2. Brainstorming.

Forms of workmaac083a7c0d6e162_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmaac083a7c0d6e162_1528450127855_0Introduction

The teacher introduces the subject of the lesson: calculating the area of the trianglearea of the trianglearea of the triangle.

Students revise the material concerning triangles and line segments in triangles.

Proceduremaac083a7c0d6e162_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to derive the formulaformulaformula for the area of the trianglearea of the trianglearea of the triangle on the basis of the formula for the area of the rectangle.

[Geogebra applet]

Conclusion:

The area of the triangle is equal to half the product of the base and the altitude of this base:maac083a7c0d6e162_1527752263647_0The area of the triangle is equal to half the product of the base and the altitude of this base:

[Illustration 1]

Task
Students calculate the area of an isosceles triangle whose arm and basebasebase are, respectively, 10 cm and 12 cm.

Task
Students together derive the formulaformulaformula for the area of the right‑angled trianglearea of the right‑angled trianglearea of the right‑angled triangle:

[Illustration 2]

Conclusion:

The area of the right‑angled trianglearea of the right‑angled trianglearea of the right‑angled triangle is equal to half the product of its cathetuses.

Task
Students calculate the area of the right‑angled triangleright‑angled triangleright‑angled triangle whose cathetusecathetusecathetuse is 4 cm and hypotenusehypotenusehypotenuse is 5 cm.

Task
Students derive the formula for the area of the equilateral trianglearea of the equilateral trianglearea of the equilateral triangle on the basis of the formulaformulaformula for its altitudealtitudealtitude:

[Illustration 3]

Conclusion:

The area of the equilateral triangle whose side is a can be expressed in the following way:maac083a7c0d6e162_1527712094602_0The area of the equilateral triangle whose side is a can be expressed in the following way:

Task
Students calculate the area of the equilateral trianglearea of the equilateral trianglearea of the equilateral triangle whose side is $4\sqrt{5}$.

An extra task
Students calculate the altitudealtitudealtitude of the equilateral triangleequilateral triangleequilateral triangle whose area is $6\sqrt{3}$.

Lesson summarymaac083a7c0d6e162_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 trianglearea of the trianglearea of the triangle:

[Illustration 1]

The area of the right‑angled triangle:maac083a7c0d6e162_1527752256679_0The area of the right‑angled triangle:

[Illustration 2]

The area of the isosceles triangle:

[Illustration 3]

Selected words and expressions used in the lesson plan

altitudealtitudealtitude

area of the equilateral trianglearea of the equilateral trianglearea of the equilateral triangle

area of the right‑angled trianglearea of the right‑angled trianglearea of the right‑angled triangle

area of the trianglearea of the trianglearea of the triangle

basebasebase

cathetusecathetusecathetuse

equilateral triangleequilateral triangleequilateral triangle

formulaformulaformula

hypotenusehypotenusehypotenuse

right‑angled triangleright‑angled triangleright‑angled triangle