Question

the figure shows a smaller square within a larger square (larger square: 10 in, smaller square: 5 in). a point is chosen at random inside the larger square. what is the probability that the point is in the shaded area? write the answer as a decimal.

Explanation:

Step1: Calculate area of larger square

The side length of the larger square is 10 in. The formula for the area of a square is \( A = s^2 \), where \( s \) is the side length. So, the area of the larger square is \( 10^2 = 100 \) square inches.

Step2: Calculate area of smaller square

The side length of the smaller square is 5 in. Using the same area formula for a square, the area of the smaller square is \( 5^2 = 25 \) square inches.

Step3: Calculate the probability

Probability is the ratio of the area of the smaller square (the favorable area) to the area of the larger square (the total area). So, the probability \( P \) is \( \frac{25}{100} = 0.25 \).

Answer:

0.25