Missing Square

[Darwinian]

Is this an optical illusion or is reality on the blink again?

Question, given that both triangles seem to occupy exactly the same area, where does the blank square come from?



Edit: And if Adrian's here, please hide the answer

[Tiberius]

Edit: Hid the answer

---

They aren't triangles, but rather very cleverly constructed quadrilaterals. For the whole shape to be a triangle, the two inner triangles must have the same angled hypotenuse, yet a simple ratio calculation shows this is impossible:

Smaller triangle: 5 units width : 2 units height.
Larger triangle: 8 units width : 3 units height.

5:2 is not the same ratio as 8:3, so the angle of the hypotenuse is different. The equation for finding the angle is:

tan(θ) = opposite / adjacent

so in the smaller triangle, this would be: tan(θ) = 2 / 5
in the larger, this would be tan(θ) = 3 / 8

As 5:2 and 8:3 are not equivalent ratios, their inverse cannot be either, so the tan(θ) will be different each time.

In the first triangle, the hypotenuses bend in towards the rest of the shape. In the second, they bend outwards, creating the extra square.

---

[theblindferrengi]

This was an easy one.

---

The figures are neither congruent nor triangles. The triangle that is made from the three acute angles along the perimiter of the figure should have a hypotenuse with a slope of 5/13. The red triangle has a hypotenuse with a slope of 3/8, and the blue triangle has a slope of 2/5. The small triangles should have slope congruent to eachother and the triangle-ish figure they make, since they dont there is an obtuse angle along the hypotenuse of the triangle-like large figure, making it an irregular tetragon.

When you switch the red and blue triangles, it changes the concave obtuse angle into a convex obtuse angle, therefore changing the area. The missing aquare comes from the sliver that is changed along the hypotenuse.

---

Edit: Damn Adrian, cut me off.

[fr0d0]

Here: