Question

1 multiple choice 1 point triangles a through h are placed in an eight by eight square as shown in the figure above. assuming a dart randomly strikes the interior region of the square, what is the probability that the dart lands in triangle a? 1/2 1/4 1/32 1/8

Explanation:

Step1: Calculate the area of the square

The side - length of the square is \(8\). Using the formula \(A = s^2\) (where \(s\) is the side - length of the square), the area of the square \(A_{square}=8\times8 = 64\).

Step2: Analyze the number of congruent triangles

The square is divided into \(8\) congruent triangles (\(A, B, C, D, E, F, G, H\)).

Step3: Calculate the probability

The probability \(P\) that the dart lands in triangle \(A\) is given by the formula \(P=\frac{\text{Area of triangle }A}{\text{Area of the square}}\). Since the \(8\) triangles are congruent, if we let the area of each triangle be \(A_{triangle}\), and \(A_{square}=\sum_{i = A}^{H}A_{triangle}=8A_{triangle}\). Then \(P=\frac{A_{triangle}}{8A_{triangle}}\) (the area of each triangle cancels out).

Answer:

\(\frac{1}{8}\)