An equilateral triangle with side length 6 cm sits on the edge of a square. Each vertex of the triangle touches an edge of the square. A point is randomly chosen on the surface. What is the probability the point lands inside the triangle? (Hint: Draw a diagram!)
*
1/4
1/3
1/2
3/4
To solve this problem, we can first calculate the area of the square and the area of the equilateral triangle.
The area of the square is side length squared, so the area of the square is 6^2 = 36 sq cm.
The area of an equilateral triangle is given by the formula:
Area = (side length^2 * sqrt(3))/4
Plugging in the side length of 6 cm, we get:
Area of equilateral triangle = (6^2 * sqrt(3))/4 = 9 sqrt(3) sq cm.
So the area of the equilateral triangle is 9 sqrt(3) sq cm.
To find the probability the point lands inside the triangle, we need to calculate the ratio of the area of the triangle to the area of the square:
Probability = 9 sqrt(3) / 36 = sqrt(3) / 4
Therefore, the probability the point lands inside the triangle is sqrt(3) / 4, which is approximately equal to 0.433 or 43.3%.
Therefore, the answer is not listed in the options you provided. The correct answer is sqrt(3) / 4, or approximately 0.433 or 43.3%.