The Finding area by composing and decomposing shapes exercise appears under the 6th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise is supposed to find the area of complex shapes by breaking them into smaller pieces.

Types of Problems

There are two types of problems in this exercise:

  1. Find the requested area: This problem describes a situation where a common geometric shape is broken into a different shape or used to create a complex shape. The user is asked to find the area of the new shape and write it in the provided space.

    Find the requested area

  2. Answer the problem by using the shape: This problem describes a situation and some shapes that are used to solve a problem. The user is asked to answer the problem and provide the solution in the space provided.

    Answer the problem by using the shape


Knowledge of the area formulas will be needed to accomplish this exercise.

  1. Many shapes can be broken into rectangles and triangles. These two shapes can then be used to find the correct area needed.
  2. Read the problems carefully. The Answer the problem by using the shape problem on this page has several flags being created so the answer is not just the area of the shape pictured.

Real-life Applications

  1. 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.
  2. Area and perimeter are used in many jobs such as architecture and interior design.

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