A Trapezium and its properties

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Concept # A Trapezium and its properties

Learning objectives

  1. A quadrangle with only two opposite sides parallel is called a trapezium, or trapezoid.
  2. The parallel sides are called the bases of the trapezium and the other two sides are called the legs or the lateral sides.
  3. If the legs are equal in length, then this is an isosceles trapezium.
  4. The distance between the bases is called height of trapezium.

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #2. Measurements in Trapezium

Learning objectives

  1. The trapeium contains two parallel sides and two non-parallel sides.
  2. The area of trapezium is found by viewing it as a parallelogram.
  3. The area of trapezium is 1/2(a+b)h where a and b are its parallel sides and h is the perpendicular distance between them.
  4. The perimeter of a trapezium is obtained by sum of its 4 sides.

Notes for teachers

  1. The area of most figures can be expressed in terms of its dimensions.
  2. The area of most composite figures can be calculated using the area of primary figures.

Activity No # 1.Area of a trapezium

  • Estimated Time: 20 minutes.
  • Materials/ Resources needed : Laptop, geogebra file, projector and a pointer.
  • Prerequisites/Instructions, if any
  1. The students should know a parallelogram and formula to find its area.
  2. They should know the trapezium and its properties.
  • Multimedia resources: Laptop
  • Website interactives/ links/ / Geogebra Applets

  • Process:
  1. The teacher can initially discuss about a trapezium.
  2. She can then reiterate that formula for area of certain composite figures can be found by converting them into known simple figures.
  3. Here the trapezium is converted into a parallelogram.
  4. Area of parallelogram is then deduced.
  • Developmental Questions:
  1. What is a trapezium ?
  2. Name its two parallel sides.
  3. What is meant by the height of the trapezium ?
  4. After cutting the trapezium exactly in the centre what would be the new height ?
  5. What is the length of the new parallelogram formed ?
  6. What is the formula to find the area of a parallelogram ?
  7. What is the area of this parallelogram formed from a trapezium ?
  • Evaluation:
  1. Explain the sequence of steps involved in deriving the formula for the area of a trapeium.
  • Question Corner:
  1. Recall the steps involved in deriving the formula for area of a parallelogram.

Concept # 3.Construction of Trapezium

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time: 40 minutes.
  • Materials/ Resources needed: a ruler, pencil, compass, and a blank piece of paper
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process:
  1. This construction can be made if the height of the trapezium along with the length of the four sides is known.
  2. Draw a straight line lightly using your ruler and pencil on your paper. - This is what is called a construction line, and will be the base of the trapezium.
  3. Indicate the two end points of the base of the shape with two points, measured by ruler.

Note:We know that the top and base line of a trapezium are parallel, and, we know the distance between them (the height).

  1. Using compass, construct two lines (lightly) perpendicular to the base. On both of these lines measure the height of the trapezium, and indicate with two points (one on each perpendicular) Connect these two points using a light construction line. The second side of the trapezium will be 'somewhere' on this line.
  2. Using ruler, measure the length of the third and fourth sides between these two paralell lines, using the points on the first construction line, as one end of the line segment. Mark with a point.

Note: You will now have four construction lines, intersecting at four vertices.

  1. The required trapezium is the shape contained between the four points of intersection of these four lines.
  2. Using a heavier line connect the four points to finish your shape.
  • Developmental Questions:
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
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  • Evaluation
  • Question Corner

Concept # 4. Isosceles trapezium

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
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  • Website interactives/ links/ / Geogebra Applets
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  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

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