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The Area of triangles exercise appears under the 6th grade (U.S.) Math Mission, Algebra basics Math Mission, High school geometry Math Mission and Mathematics I Math Mission. This exercise introduces the area of a triangle.

Types of Problems

There are two types of problems in this exercise:

  1. Compare the areas of the triangles: This problem provides two triangles draw on lattice grids. The user is asked to determine which, if either, of the triangles has the largest area.
    Aot1

    Compare the areas of the triangles

  2. Find the area: This problem provides a triangle that has all of its sides and the height labeled. The user is asked to find the area of the triangle and place the answer in the space provided.
    Aot2

    Find the area

Strategies

Knowledge of the general area of a triangle formula is needed to complete this exercise.

  1. The formula for the area of a triangle is {\frac{(b\times h)}{2}}, or {\frac{1}{2}\times (b\times h)}.
  2. Several of the Compare the areas of the triangles are equal. All that is needed to see this is to compare the heights and the bases.
  3. Some of the triangles can be compared visually instead of numerically to see which is bigger because the pictures are always drawn to scale.

Real-life Applications

  1. Architects use lots of geometry when building bridges, roofs on houses, and other structures.
  2. 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.
  3. Triangles will appear in the Pythagorean Theorem.

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