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The area of the trapezium

Source: licencja: CC 0.

Pole trapezu

Learning objectives

  • You will learn to calculate the area of the trapezium.

  • You will learn to calculate the lengths of the sides of the trapezium of a given area.

Learning effect

  • You calculate the area of the trapezium.

  • You calculate the lengths of the sides of the trapezium of a given area.

Task 1
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nagranie abstraktu

Open the applet and determine the formulaformulaformula for the area of the trapezium. Is there some other way to determine the area of the trapezium? Check your assumptions by making appropriate drawings.

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Geogebra aplet - pole trapezu. Galeria z opisami alternatywnymi poniżej.
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

Notice that the area of the trapezium is equal to the product of half of the sum of its bases and its altitude.

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nagranie abstraktu

Conclusion:

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

P=a+b2h
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Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

Use the derived formulaformulaformula in the following exercises.

Task 2
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nagranie abstraktu

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

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Source: GroMar, licencja: CC BY 3.0.
Task 3
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nagranie abstraktu

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 4
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nagranie abstraktu

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

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Source: GroMar, licencja: CC BY 3.0.
Task 5
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nagranie abstraktu

An extra task:

Calculate the area of the regular hexagon whose side is 4 dm.

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nagranie abstraktu

Do the revision exercises.

Exercises

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Exercise 1
Wersja alternatywna ćwiczenia: In the trapezium, one of the sides is 13 cm and each of the other sides is 5 cm. The area of the trapezium is: Możliwe odpowiedzi: 1. 54 cm², 2. 27 cm², 3. 272 cm², 4. 273 cm²
Exercise 2

Calculate the perimeter of the right‑angled trapezium ,whose bases are equal to 6 cm and 14 cm, and the area is 50 cmIndeks górny 2.

Exercise 3

The altitude of the trapezium is 4 cm. The diagonals of the trapezium are equal and cross at the right angle in their mid‑points. Calculate the area of the trapezium.

Describe the solution in English.

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Exercise 4
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. pole trapezu - the area of the trapezium, 2. trapez prostokątny - the right-angled trapezium, 3. trapez równoramienny - the isosceles trapezium, 4. wysokość trapezu - the altitude of the trapezium, 5. obwód trapezu - the formula, 6. wzór - the perimeter of the trapezium
zadanie
Source: GroMar, licencja: CC BY 3.0.
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Glossary

formula
formula

wzór

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wymowa w języku angielskim: formula
isosceles trapezium
isosceles trapezium

trapez równoramienny

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wymowa w języku angielskim: isosceles trapezium
the altitude of the trapezium
the altitude of the trapezium

wysokość trapezu

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wymowa w języku angielskim: the altitude of the trapezium
the area of the trapezium
the area of the trapezium

pole trapezu

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wymowa w języku angielskim: the area of the trapezium
the perimeter of the trapezium
the perimeter of the trapezium

obwód trapezu

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wymowa w języku angielskim: the perimeter of the trapezium
the right‑angled trapezium
the right‑angled trapezium

trapez prostokątny

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wymowa w języku angielskim: the right‑angled trapezium
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Keywords

the area of the trapeziumthe area of the trapeziumthe area of the trapezium is expressed with the formula P=a+b2h

isosceles trapeziumisosceles trapeziumisosceles trapezium – trapezium whose legs are equal and it is not a parallelogram

the right‑angled trapeziumthe right‑angled trapeziumthe right‑angled trapezium – a trapezium that has at least one 90° angle

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