Base (Triangle)

Elementary School

Definition

In a triangle, any side of it can be a base. However, the base and the height of the triangle must be perpendicular to one another. The height of a triangle is the line from the vertex to the opposite side of the triangle that is perpendicular.

Worked examples

\(\)Area\( = \frac{1}{2} \times \)base\( \times \)height\( = \frac{1}{2} \times 8 \times 5 = 20\)

Pick any side as the base (here 8 units); the height (5 units) must be perpendicular to it.

\(\)Same triangle, new base: Area\( = \frac{1}{2} \times 6 \times \frac{20}{3} = 20\)

Choosing a different side as base changes the height value but gives the same area.

Common mistakes

Using a slanted side length as the height → The height must be perpendicular to the base Height is always measured at a right angle to the base, not along another side.
Thinking only the bottom side can be the base → Any of the three sides can serve as the base Rotate the triangle in your mind; whichever side you treat as base, draw the perpendicular height to it.

Where you'll use it next

Understanding base and height is essential for finding areas of triangles, then parallelograms and trapezoids. You'll also apply it in trigonometry when working with sine for area and in coordinate geometry proofs.

Found in 1 StudyPug lesson

Triangle Area and Perimeter: Mastering Fundamental Geometry

Grade 5 Math placeholder

Unlock the power of triangle geometry! Learn to calculate area and perimeter with confidence. Perfect for students seeking to enhance their math skills and tackle real-world problems.

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