Area of a Triangle – Identifying Dimensions

Area of a Triangle is usually taught in 5th grade. While the basic formula (1/2 base x height) and its proof are not hard to understand, students often have trouble identifying what or where the “base” and “height” are.

Specifically, they may have difficulty finding suitable line segments (with start and end points) to measure these dimensions off. As a convention, we usually assign one side of a triangle to be its base, so the main problem is constructing the perpendicular line segment that can be used to measure the height.

To help with this, we often ask students to identify the line segments to measure heights, given different assignment of the base (may or may not be of different types or orientation), e.g.

A slightly more confusing example is the obtuse triangle, where the line segment may sometimes be constructed outside the triangle.

(It is also fun to let students work out the proof of the area formula for obtuse triangle visually)

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