1. The area shown below will be used for the elementary school playground. What is this area? How much fencing is needed to enclose the playground? Use 3.14 for the value of pi. d= 4 yds for the half circle, w=10 yds. for width of rectangle, and length = 4 yds. and 3 yds for the base of the triangle. Can someone help me to understand this problem?
We are unable to visualize the diagram.
To understand this problem, let's break it down step by step:
Step 1: Determine the area of the entire playground.
The playground consists of a half circle (with a diameter of 4 yards) and a rectangle (with a width of 10 yards and a length of 4 yards). To find the area of the half circle, we can use the formula A = π * r^2 / 2, where r is the radius (half of the diameter). So, the radius of the half circle is 4/2 = 2 yards. Plugging in the values, we have A = 3.14 * 2^2 / 2 = 3.14 * 4 / 2 = 3.14 * 2 = 6.28 square yards.
Next, to find the area of the rectangle, we can use the formula A = length * width, which gives us A = 4 * 10 = 40 square yards.
To find the total area of the playground, we need to add the areas of the half circle and the rectangle: 6.28 + 40 = 46.28 square yards.
Step 2: Determine the amount of fencing needed to enclose the playground.
To calculate the perimeter of the half circle, we use the formula P = π * d, where d is the diameter. In this case, the diameter is 4 yards, so P = 3.14 * 4 = 12.56 yards.
The perimeter of the rectangle is calculated using the formula P = 2 * (length + width), which gives us P = 2 * (4 + 10) = 2 * 14 = 28 yards.
Finally, to calculate the perimeter of the triangle, we simply add up the lengths of its three sides: 4 + 3 + 3 = 10 yards.
To find the total amount of fencing needed, we add up the perimeters of the half circle, rectangle, and triangle: 12.56 + 28 + 10 = 50.56 yards.
Therefore, you need approximately 50.56 yards of fencing to enclose the elementary school playground.