Area of a Parallelogram

The area of a parallelogram is the base times the height drawn to it: S = a · h.

Where the formulas come from. All area formulas grow out of the rectangle's a · b. A parallelogram rearranges into a rectangle, a triangle is half a parallelogram, a trapezoid is its “average width” times the height. The circle's πr² comes from slicing the circle into thin sectors. The calculator shows the formula and the substitution for every shape — ready to copy into a notebook.

FAQ

How do you find a triangle's area from the sides alone?

With Heron's formula: compute the semi-perimeter p = (a + b + c) / 2, then the area is the square root of p(p−a)(p−b)(p−c). No height needed. The calculator has a switch for this method.

What value of π should I use?

π ≈ 3.14159… School problems usually take 3.14; the calculator uses higher precision. If the problem says “take π = 3.14”, the answer may differ slightly from the calculator's — that is normal.

What units does the area come in?

Square units: dimensions in centimeters give cm², in meters — m². Just make sure all dimensions of one shape use the same unit.

Why isn't a parallelogram's area the product of its sides?

Because it leans: the height is shorter than the slanted side. The product of the sides would be the area of a rectangle with those sides, and a parallelogram with the same sides is always “lower”. Hence the height in the formula: S = a · h.