What are the Formulas for the Area of a Triangle and a Parallelogram?
To calculate the exact surface area of geometric shapes without counting grids, we use specific mathematical formulas based on two crucial measurements: the base and the height.
- The base is any chosen side of the shape on which it appears to stand.
- The height (also known as the altitude) is the shortest perpendicular straight line drawn from the opposite corner down to that chosen base line, meeting it at a right angle (90°).
Let us break down the formulas for our two key shapes:
- Area of a Parallelogram: A parallelogram is a four-sided shape where opposite sides run parallel to each other. The area is simply found by multiplying the base by the corresponding perpendicular height.
Formula: Area = base × height
- Area of a Triangle: A triangle can be thought of as exactly half of a parallelogram. If you draw a diagonal line through a parallelogram, it splits it into two congruent triangles. Because it is half the size, its area formula includes a fraction of a half.
Formula: Area = 0.5 × base × height
A crucial rule to remember is that the height must always match its corresponding base. If you use a different side as your base, you must use the specific altitude that drops vertically onto that new side.