Question

Given a circle with an inscribed equilateral triangle with each side of the triangle having a measurement of 18 cm. What is the probability of selecting a point at random inside the triangle, assuming that the point cannot lie outside the circular region.

Answer 1

To be able to answer this question, you have to know the areas of the triangle and the circle. If the area of the triangle is a, and the area of the circle is c, the probability of selecting a point inside the triangle is a/c.

I have included a drawing. In it, r is the radius of the circle. We need to know r if we want to calculate the area.

If you look at triangle MDB, you'll see it must be a 30-60-90 triangle.
This means, because you know ONE side (BD=9), you can calculate both it's other sides, so including r.

The all-important question here is: do you know what a 30-60-90 triangle is (and what the ratio of its sides are)?