Question

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 or b?
\\(\frac{1}{16}\\)
\\(\frac{1}{4}\\)
\\(\frac{1}{8}\\)
\\(\frac{1}{2}\\)

Explanation:

Step1: Find square side length

From axes, side length $= 4 - (-4) = 8$

Step2: Calculate square area

Area $= 8 \times 8 = 64$

Step3: Find triangle A/B base/height

Each triangle has base=4, height=4

Step4: Calculate area of 1 triangle

Area $= \frac{1}{2} \times 4 \times 4 = 8$

Step5: Total area of A + B

Total $= 8 + 8 = 16$

Step6: Compute probability

Probability $= \frac{16}{64} = \frac{1}{4}$

Answer:

$\frac{1}{4}$