Question

Each side of the square below is 8 inches.

A triangle inside of a square. The top of the triangle divides a side of the square into 2 equal parts of 4 inches. The triangle is shaded and the area to the right of the triangle is shaded.

What is the probability that a point chosen at random in the square is in the blue region?
0.25
0.33
0.66
0.75

Answer 1

Place the square with corners (0,0), (8,0), (8,8), (0,8). The triangle has vertices (0,0), (8,0), (4,8) (apex at midpoint of the top side). Its area = (base·height)/2 = (8·8)/2 = 32.

The region to the right of the triangle is the triangle with vertices (4,8), (8,8), (8,0); its area = (4·8)/2 = 16.

Total shaded area = 32 + 16 = 48. Square area = 64, so the probability = 48/64 = 3/4 = 0.75.