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Lesson 85: Area of a Triangle, Parallelogram, and Trapezoid
In this lesson, we'll learn how to determine the area of a triangle, parallelogram, and trapezoid. These shapes are a bit more complicated than the squares and rectangles we've been working with.
The
area of a triangle is defined as:
A = (1/2)bh. This means multiply the base times the height of
the triangle, and then multiply the result by 1/2. Stated
another way, multiply the base times the height, then divide by 2.
Look at the diagrams at right. The height is defined as the
distance from the highest point on the triangle, down to the base.
The
reason for the formula is that a triangle is really half a rectangle
or square. You can best see this by looking at the first
triangle. It actually takes up half the space of a rectangle
with the dimensions shown. If it was a rectangle, we would
just multiply the two dimensions, but since it's half, we have to
halve the result. This will help you memorize the formula.
It works for all triangles, even odd looking ones like the one on
the right. Be sure to notice how we measured the height on
that triangle.
Finding
the area of a parallelogram is easy. A parallelogram is just a
slanted rectangle (see picture at right), so the area is just A = bh.
We just multiply the two dimensions like we would for a rectangle.
The fact that it's slanted doesn't change the area.
To
find the area of a trapezoid (see picture at right), we find the
average of the two bases, and then multiply by the height.
This works because it's not exactly a rectangle, but if we average
the two bases, we can calculate the area as though it was a rectangle.
The formula is given by: A = h · (b1 + b2)/2.
Memorize these formulas, since you'll run into them in various test questions.
Remember that you can ask a math question if you have additional questions about a topic, or you can contact me if you have any comments or suggestions for this site.