Parallelogram Area Calculator
Find the area of a parallelogram from its base and perpendicular height, and its perimeter when you also give a side length.
How it works
Area = base · height · Perimeter = 2 · (base + side)
A parallelogram is a rectangle that has been sheared sideways, and shearing does not change area. So its area is simply the base times the perpendicular height — the straight-across distance to the opposite side, not the length of the slanted edge. The perimeter, on the other hand, needs the actual side length: twice the base plus twice the adjacent side, because opposite sides are equal.
Worked example
With base 6 and perpendicular height 4, the area is 6 × 4 = 24 square units. If the slanted side measures 5, the perimeter is 2 × (6 + 5) = 22 units. Note the height (4) is shorter than the slanted side (5) because the side leans.
Sources: Parallelogram — Wikipedia
Frequently asked questions
Why use the height instead of the slanted side for area?
Area depends only on how far apart the two parallel bases are, which is the perpendicular height. The slanted side is longer than that gap, so using it would overstate the area. Slide the top edge sideways and the area stays fixed even as the sides lengthen.
How do I get the height if I only know the side and an angle?
Multiply the slanted side by the sine of the angle it makes with the base: height = side × sin(angle). A side of 5 at 53° gives a height of about 5 × 0.7986 ≈ 4.
Is a rectangle a parallelogram?
Yes. A rectangle is a parallelogram whose angles are all 90°, so its height equals its side and area = base × height reduces to length × width.
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This calculator is for educational purposes. Double-check important results before acting on them.