Standard #: MA.5.G.5.4 (Archived 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
Supporting Idea: Geometry and Measurement - Geometry and Measurement
Date Adopted or Revised: 09/07
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)
    N/A

    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 # Question Difficulty Type
Sample Item 1 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?
N/A MC: Multiple Choice


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