Question

the target in the figure shown to the right contains four squares. if a dart thrown at random hits the target, find the probability that it will land in a green region.
the probability that a dart will land in a green region of the square target is . (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate area of whole target

The side - length of the outermost square is 24 inches. The area of a square is $A = s^2$, so the area of the whole target $A_{total}=24^2 = 576$ square inches.

Step2: Calculate area of inner non - green square

The side - length of the innermost non - green (blue) square is 18 inches. Its area $A_{1}=18^2=324$ square inches.

Step3: Calculate area of second non - green square

The side - length of the second non - green (blue) square (outermost blue) has side - length 6 inches. Its area $A_{2}=6^2 = 36$ square inches.

Step4: Calculate total non - green area

The total non - green area $A_{non - green}=A_{1}+A_{2}=324 + 36=360$ square inches.

Step5: Calculate green area

The green area $A_{green}=A_{total}-A_{non - green}=576-360 = 216$ square inches.

Step6: Calculate probability

The probability $P$ that the dart lands in the green region is $P=\frac{A_{green}}{A_{total}}=\frac{216}{576}=\frac{3}{8}$.

Answer:

$\frac{3}{8}$