Topicmc6dbad9920643dbd_1528449000663_0Topic

Calculating the area of the polygon

Levelmc6dbad9920643dbd_1528449084556_0Level

Second

Core curriculummc6dbad9920643dbd_1528449076687_0Core curriculum

XI. Calculations in geometry. The student:

4) calculates the area of the polygons using the method of dividing them into smaller polygons or adding elements to get larger polygons (…).

Timingmc6dbad9920643dbd_1528449068082_0Timing

45 minutes

General objectivemc6dbad9920643dbd_1528449523725_0General objective

Noticing regularities, similarities and analogy as well as formulating conclusion based on them.

Specific objectivesmc6dbad9920643dbd_1528449552113_0Specific objectives

1. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

2. Calculating the area of any polygons using the method of dividing them into smaller polygons.

3. Noticing the relationships between the perimeter of the polygon and its area.

Learning outcomesmc6dbad9920643dbd_1528450430307_0Learning outcomes

The student:

- calculates the area of any polygons using the method of dividing them into smaller polygons, whose area can be easily calculated,

- notices the relationship between the perimeter of the polygonperimeter of the polygonperimeter of the polygon and its area.

Methodsmc6dbad9920643dbd_1528449534267_0Methods

1. Case study.

2. Open ear.

Forms of workmc6dbad9920643dbd_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc6dbad9920643dbd_1528450127855_0Introduction

The students use the „open ear” technique to revise the formulae and the most important concepts useful when calculating the areas of polygons.

The teacher specifies the aim of the class – calculating the area of the polygonarea of the polygonarea of the polygon, which is neither a triangle nor a quadrangle.

Proceduremc6dbad9920643dbd_1528446435040_0Procedure

The students work in small groups using the “case study” technique. Every group gets a piece of paper with a polygonpolygonpolygon on it. The teacher informs the students that a friend of his asked him to help him with calculating the surface area of the garden plot that he has got. The plot has the shape of the figure on the piece of paper. This person would like to take as few measurements as possible. Every group has to suggest a method of calculating the area.

After the time limit, the groups present their solutions. They cooperate to decide what the best method of calculating the area of irregular polygons is. They formulate a conclusion.

The conclusion

You can calculate the area of any polygon using the method of dividing it into smaller polygons or adding elements to get a larger polygon.

They use the conclusion to solve the tasks.

Task 1

A hexagon is made of two identical isosceles trapezoids. The altitudes of these trapezoids equal 10 cm, and their bases 25 cm and 15 cm. Calculate the area of this hexagon.mc6dbad9920643dbd_1527752263647_0A hexagon is made of two identical isosceles trapezoids. The altitudes of these trapezoids equal 10 cm, and their bases 25 cm and 15 cm. Calculate the area of this hexagon.

Students observe the relationship between the polygon's circumference and its area. Save your application.

[Illustration 1]

The conclusion that should be drawn by the students.

The polygons with the same perimeters may have different areas.

The students do the tasks using the information.

Task 2

Draw any 3 polygonpolygonpolygon, not being rectangles, on a squared sheet of paper. Each of them should have the surface area of 18. Calculate the perimeter of each of them. Assume a side of the squaresquaresquare as your unit.

Will the perimeter of the polygonperimeter of the polygonperimeter of the polygon change when you change its shape, and the area will remain the same?

Task 3

A diagonal divides a trapezoid into two triangles. The area of the bigger one is twice as big as the area of the smaller triangle. How many times is the area of the whole trapezoid larger than the area of the smaller triangle?mc6dbad9920643dbd_1527752256679_0A diagonal divides a trapezoid into two triangles. The area of the bigger one is twice as big as the area of the smaller triangle. How many times is the area of the whole trapezoid larger than the area of the smaller triangle?

An extra task:

The surface area of a rectangular stamp equals 12 cmIndeks górny 2². What are the dimensions of this stamp if its length is three times larger than its width?

The students work in small groups and find relationships between the area of the rectanglerectanglerectangle and its perimeter. They formulate hypotheses and check them using their computers.

[Geogebra applet]

The conclusion that should be drawn by the students.

The squaresquaresquare has the smallest perimeter among all rectangles with equal areas.

The students solve the tasks individually, using the property they have just observed.

Task 4

Jurek wants to buy a rectangular garden plot, whose area equals 1000 mIndeks górny 2². He wants to surround it with the smallest possible amount of a wire fence. What dimensions should this plot have?

Lesson summarymc6dbad9920643dbd_1528450119332_0Lesson summary

The students do the consolidation tasks. Next, they summarize the class and formulate the conclusions that they should remember.

- The polygons with the same perimeters may have different areas.

- The squaresquaresquare has the smallest perimeter among all rectangles with equal areas.

Selected words and expressions used in the lesson plan

area of the polygonarea of the polygonarea of the polygon

perimeter of the polygonperimeter of the polygonperimeter of the polygon

polygonpolygonpolygon

rectanglerectanglerectangle

squaresquaresquare

trapezoidtrapezoidtrapezoid