Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.).
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
Standard: Polygons - Identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. Find measures of angles, sides, perimeters, and areas of polygons, justifying the methods used. Apply transformations to polygons. Relate geometry to algebra by using coordinate geometry to determine transformations. Use algebraic reasoning to determine congruence, similarity, and symmetry. Create and verify tessellations of the plane using polygons.
Date Adopted or Revised: 09/07
Date of Last Rating: 06/07
Status: State Board Approved
Assessed: Yes


Example 1: A rectangle of area 360 square yards is ten times as long as it is wide. Find its length and width.

Example 2:  Explain the derivation of the formula for the area of a triangle.

Example 3: The design below is called the Ohio Star. Assuming that it measures 9 inches by 9 inches, calculate the total area of all the orange patches, the total area of all the yellow patches, and the total area of all the green patches. How much fabric of each color will you need to cover an area that measures 72 inches by 90 inches?



  • Reporting Category: Geometry
  • Item Type(s): This benchmark will be assessed using: MC , FR item(s)
    Also Assesses:

    MA.912.G.2.7 Determine how changes in dimensions affect the perimeter and area of common geometric figures.

  • Clarification :
    Students will solve problems by using and/or deriving formulas for perimeter and/or area of polygons.
  • Content Limits :

    Items requiring students to calculate area may require the use of the apothem.

    Composite figures may include circles.

  • Stimulus Attributes :

    Items may be set in either mathematical or real-world contexts.

    Graphics should be used in most of these items, as appropriate.


  • Test Item #: Sample Item 1
  • Question:

    Marisol is creating a custom window frame that is in the shape of a regular hexagon. She wants to find the area of the hexagon to determine the amount of glass needed. She measured diagonal d and determined it was 40 inches. A diagram of the window frame is shown below.


    Which of the following is closest to the area, in square inches, of the hexagon?

  • Difficulty: N/A
  • Type: MC: Multiple Choice

  • Test Item #: Sample Item 2
  • Question:

    A package shaped like a rectangular prism needs to be mailed. For this package to be mailed at the standard parcel-post rate, the sum of the length of the longest side and the girth (the perimeter around its other two dimensions) must be less than or equal to 108 inches (in.). Figure 1 shows how to measure the girth of a package.


    What is the sum of the length, in inches, of the longest side and the girth of the package shown in Figure 2?

  • Difficulty: N/A
  • Type: FR: Fill-in Response