Question

al of
10. A square field has four sprinklers that spray
in the areas represented by the circles below. If
the shaded portion represents area that is not
reached by the sprinklers, find the total area that
is not reached by the sprinklers.

Answer 1

Using the areas of the sqaure and of the circle, it is found that the total area that is not reached by the sprinklers is of 343.36 ft².

What is the area of a square?

The area of a square of side length l is given by:

A = l²

In this problem, we have that l = 40 ft, hence:

A = (40 ft)² = 1600 ft².

What is the area of a circle?

The area of a circle of radius r is given by:

$A = \pi r^2$

In this problem, we have four circles of radius r = 10 ft, hence it's combined area, in square feet, is given by:

$A_c = 4\pi (10)^2 = 400\pi = 1256.64 \text{ft}^2$

The area not reached by the sprinklers is the subtraction of the area of the square by the area of the circle, hence:

1600 - 1256.64 = 343.36 ft².

More can be learned about the area of a rectangle at https://brainly.com/question/10489198