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Area of a Parallelogram
Rung 3 of 4 · The traps

The Slant Is Not the Height

This is the parallelogram mistake. The slanted side is sitting right there, looking like a height — but use it and your answer is always too big.


ExploreLean the shape over. Watch the slant grow while the true height — and the area — stay put.
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A diagram of a parallelogram usually labels the slanted side and the perpendicular height. Both are lengths, both look like they could be "the height" — but only one belongs in the formula.

Two Different Lengths

The slanted side is the actual sloping edge of the shape. The perpendicular height is the distance straight up from the base to the top, at a right angle. Because the slant goes across as well as up, it's always the longer of the two. The formula needs the upright one — that's the height of the hidden rectangle from rung 1.

Say it plainly: use the height that makes a right angle with the base (the dashed line), never the sloping side. Slant = trap.

The Proof They're Different

Press "lean it over" and keep leaning. The slanted side stretches longer and longer, but the perpendicular height doesn't move — and neither does the area. So the slant can be anything while the area stays fixed; that's how you know the slant can't be the thing that sets the area. Only the perpendicular height does.

Spotting It in a Question

Look for the little right-angle square. The length attached to that line is your height. Any length running along a sloping edge is a decoy — examiners put it there on purpose. If you ever multiply base by a slant, you'll get a number that's too big, and that's the giveaway you grabbed the wrong one.

Us, Thinking Out Loud

Why is the slanted side always longer than the perpendicular height?

If using the slant makes the answer too big, what does that tell us about which length is "real"?