Exercise 51 Page 905

We are given a diagram and asked to find the area of the shaded region. Let's take a look at the diagram.

To find the area of the shaded region, we will subtract the area of the square from the area of the circle. To do so, let's first find the area of the square. We can see from the diagram that the length of the side of the square is 10m. Recall the formula for the area S of a square with side length a. S = a^2 By substituting 10 for a in this formula, we will find the area of the square. The area of the square is 100 square meters. To find the area of the circle, note that the diagonal of the square is the diameter of the circle. Since the length of the diagonal of a square is sqrt(2) times the length of the side of the square, the diameter of our circle is 10sqrt(2)m. The radius of a circle is half of its diameter, so the radius of our circle is 5sqrt(2) m. Recall the formula for the area C of a circle with radius r. C = π r^2 By substituting 5sqrt(2) for r in this formula, we will find the area of the circle. Now we can calculate the area of the shaded region by subtracting the area S of the square from the area C of the circle. The area of the shaded region rounded to the nearest tenth is 57.1 m^2.