The Area of quadrilaterals and polygons exercise appears under the 6th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise uses the various area formulas to answer problems.

Types of Problems

There are three types of problems in this exercise:

  1. Find the area of the shape on the grid: This problem has a polygon placed on a grid. The user is asked to find the area of the polygon and write it in the space provided.

    Find the area of the shape on the grid

  2. Find the area by breaking the shape: This problem has a complex polygon that can be clearly split into several simpler polygons such as rectangles and triangles. The user is asked to find the total area and write it in the space provided.

    Find the area by breaking the shape

  3. Compare the shapes: This problem has a given polygon with a fixed area and several other polygons. Users are asked to select which of the polygons has the same area as the given polygon.

    Compare the shapes


Knowledge of area formulas, especially rectangle and triangle, are needed to complete this exercise.

  1. The area of a rectangle is base times height, and the area of a triangle is half that.
  2. On the grid, find the area of the overall rectangle that can be constructed around the polygon, then subtract by the right triangles that are removed in each "corner."
  3. On the Compare the shapes problem it is possible to break apart the given polygon and maneuver it to look like the correct answer. This geometric view can increase ability to work with the shapes.

Real-life Applications

  1. Area and perimeter are used in many jobs for architecture and interior design.
  2. Architects use these shapes when building bridges, roofs on houses, and other structures.
  3. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.

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