Identifying Base and Height
For any triangle, the base and height must be perpendicular to each other — they meet at exactly 90 degrees. In a right triangle, the two legs that form the right angle are automatically the base and height. For other triangles, the height is the perpendicular segment from the base to the opposite vertex, which may fall outside the triangle for obtuse shapes. This concept from Reveal Math, Course 1, Module 8 is essential for correctly applying the triangle area formula A = (1/2)bh in 6th grade.
Key Concepts
Property When calculating the area of any triangle, the base and height must be perpendicular to each other. This means the lines representing the base and height must intersect to form a perfect 90° right angle, often marked with a small square symbol.
Examples In a right triangle, the two sides that form the right angle are already the base and height. You don't need to draw any new lines inside the shape! For a triangle with a slanted side of 12 cm but a straight, perpendicular height of 9 cm measured from its 10 cm base, you must use the 9 cm. The area is 1/2 x 10 x 9 = 45 square cm.
Explanation You cannot measure a triangle's height along a slanted side! The height must be the straight up, shortest distance from the base line to the opposite tip (vertex). Think of measuring a person's height—they have to stand up completely straight, not lean over. In some wide (obtuse) triangles, you might even have to measure the height outside the triangle!
Common Questions
How do I identify the base and height of a triangle?
The base is any side of the triangle. The height is the perpendicular distance from that base to the opposite vertex, always forming a 90-degree angle with the base.
Can I use any side as the base of a triangle?
Yes, any side can be the base, but you must use the height that corresponds to that base — the perpendicular distance from that base to the opposite vertex.
Where is the height of an obtuse triangle?
For an obtuse triangle, the height from the base to the obtuse vertex falls outside the triangle. You must extend the base line and draw the perpendicular height externally.
Why can I not use a slanted side as the height of a triangle?
A slanted side is not perpendicular to the base. Using it gives a larger measurement than the true height, producing an incorrect area that is too large.
In a right triangle, which sides are the base and height?
In a right triangle, the two legs that form the right angle are the base and height. No additional construction is needed — those two sides are already perpendicular to each other.
When do 6th graders learn to identify triangle base and height?
This is covered in Module 8 of Reveal Math, Course 1, as part of the triangle area unit.