Question

The figure shows a smaller square within a larger square. A point is chosen at random inside the larger square. What is the probability that this point is in the shaded area? Write the answer as a decimal.

Answer 1

Given:

Side length of larger square = 10 in

Side length of smaller square = 5 in

To find:

The probability that this point is in the shaded area.

Solution:

Area of square formula =  side²

Area of larger square = 10²

                                     = 100 in²

Area of smaller square = 5²

                                     = 25 in²

Shaded area = Area of larger square - Area of smaller square

                      = 100 in² - 25 in²

Shaded area = 75 in²

$\text{P(point in shaded area)}=\frac{\text{Shaded area}}{\text{Total area}}$

                                     $=\frac{75}{100}$

                                     = 0.75

The probability of point in shaded area is 0.75.