MA.5.G.5.4Archived Standard

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Derive and apply formulas for areas of parallelograms, triangles, and trapezoids from the area of a rectangle.

Remarks

The formula for the area of a rectangle, "base x height", can be applied to develop formulas for the area of parallelograms, triangles, and trapezoids. Triangles can be constructed from diagonals of parallelograms to explore the formula "base x height divided by 2".
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 5
Body of Knowledge: Geometry
Idea: Level 3: Strategic Thinking & Complex Reasoning
Supporting Idea: Geometry and Measurement - Geometry and Measurement
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC item(s)

  • Clarification :
    Students will find the areas of parallelograms, triangles, and trapezoids.

    Students will justify the area formulas for parallelograms, triangles, and trapezoids using the area formula for rectangles.
  • Content Limits :
    Items assessing areas of trapezoids must use only isosceles trapezoids.

    Areas must include whole numbers with three or fewer significant digits and up to a maximum of five digits.
  • Stimulus Attributes :

    Graphics must be used in all these items.

    Items that are set in a real-world context may use length and width as dimensions as well as base and height as dimensions.

    Graphics of figures may include dashed lines that show how a shape can be decomposed and recomposed to form a rectangle.

    Figures should be presented on grids, when appropriate.

Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question: A drama teacher drew up plans for a stage he wants to build. A diagram of the top of the stage, which is in the shape of a trapezoid, is shown below.

    Trapezoid

    which is the area of the top of the stage?
  • Difficulty: N/A
  • Type: MC: Multiple Choice

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Alternate version of this benchmark for students with significant cognitive disabilities.

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