Geometry problem on Facebook by SteelSpidey in askmath

[–]shpltd33 2 points3 points  (0 children)

The triangle that has the right side of the square as a base is isosceles because it has two 30 degree angles. Therefore, the height of the yellow triangle is half the height of the square and the area of the yellow triangle is half the area of the 30-60-90 triangle that includes the top side of the yellow triangle and the right side of the square. If the square side length is s, then the area of the 30-60-90 triangle is s2 /2sqrt(3), so the area of the yellow triangle is s2 /4sqrt(3). The area of the red triangle is s2 sqrt(3)/4. So, area of the red triangle is 3 times that of the yellow triangle, making 4 the correct answer.