Areas of Geometric Shapes with the Same Perimeter

A triangle, square, hexagon, and circle all have a perimeter of one unit. Eighth graders must attempt to find the area of each and arrange them in order from least to greatest areas. A terrific task for applying four different area formulas, beginning only with the value of the perimeter. 

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CCSS: Designed
Concepts

Pros

  • The use of the Pythagorean theorem to find the area of the triangle aligns the task to Common Core State Standards
  • A thorough commentary is provided, including complete solutions for each shape
Cons

  • None
Common Core