A Simple Geometry Problem That Actually Matters in Revit
Recently, I had a telling moment. I asked someone to estimate the area of a simple shape, and they completely froze. At first glance, it seemed like a basic school problem, nothing complicated.
That’s when it hit me again: basic geometry rules are not just theory from a textbook. They’re essential, especially when we work in Revit. After all, not every element there can calculate area “by default.” You often need to bring in logic and formulas.
So I decided to break this case down step by step and show how valuable even the simplest geometry can be. I’m sure you’ll find a couple of useful ideas in this example.
Imagine a façade built from triangular and rhombus-shaped panels. At the base, we have five isosceles triangular panels in a row, with base lengths of 1200, 1300, 1400, 1500, and 1600 mm.
Here’s where it gets interesting: from each pair of triangles, a rhombus panel is built upward. Then another row of rhombuses, and so on, until the entire structure narrows to one panel at the very top. That final top panel isn’t just any rhombus - it’s a square.
❓ Question: What is the area of that top square?
There are several ways to solve this, but let’s take one of the simplest.
Since the top panel (marked in blue) is a square, all of its sides are equal, and each corner measures exactly 90°.
Now, here’s the key: every time we move upward from the triangles, the panels are rhombuses. And that brings us to an important property:
Rule: A rhombus is a parallelogram where all four sides are equal.
This means the side of the top square X has the same length as the slanted sides of the base triangles-whether that’s 120 or 160 cm.
Look at the left triangle: its side determines the side of the square.
And since the same logic applies on the right, the side of the right triangle also matches the side of the top square.
If you strip everything down to just these three shapes, it becomes clear: the sides of the triangles are parallel to the sides of the square (since rhombuses connect them). This means that when you align the triangles, the angle between their sides is exactly 90°:
Now let’s draw a height in each triangle. Recall: in an isosceles triangle, the height splits the base exactly in half:
Here’s the trick: since we already have a 90° angle, the other two angles must add up to 90° as well:
Take the right half of the left triangle. One angle is already 90°, so the remaining two must total 90°. That makes its top angle equal to the green angle in the neighboring triangle (and vice versa). Which means they’re congruent triangles! On top of that, they share the same hypotenuse: the square’s side X.
And if the triangles are congruent, then it’s straightforward: their legs just swap places, 60 cm and 80 cm (see the figure above).
Did you enjoy this simple geometry breakdown? Would you like to see more examples like this? 🙂