An equilateral triangle with side length six CM sits on the edge of a square each vertex of the triangle touches an angle of the square a point is randomly chosen on the surface. What is the probability the point lands inside the triangle?

Answer 1

To calculate the probability that a randomly chosen point on the surface lands inside the equilateral triangle, we need to compare the area of the equilateral triangle to the area of the square.

The area of the square is $(6 \text{ cm})^2 = 36 \text{ cm}^2$.

The area of an equilateral triangle can be found using the formula: $\frac{\sqrt{3}}{4} s^2$, where $s$ is the length of the side of the triangle.

So, the area of the equilateral triangle is $\frac{\sqrt{3}}{4} (6 \text{ cm})^2 = 9\sqrt{3} \text{ cm}^2$.

Therefore, the probability that a randomly chosen point will land inside the equilateral triangle is $\frac{9\sqrt{3}}{36} = \frac{\sqrt{3}}{4} \approx 0.433$.