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Geometry Problem Set

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The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, as shown in the diagram attached. See attached file for full problem description.

Solve the following problems in a Word document.

1. A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including base and the center pole are to be made of aluminum tubing. How many feet of tubing should the team buy? How many square feet of the backstop must be covered by a screen?

2. An Indian sand painter begins his picture with a circle of dark sand. He then inscribes a square with a side length of 1 foot inside the circle. What is the area of the circle?

3. Three buildings abut as shown in the diagram below. What are the dimensions of the courtyard and what is the perimeter of the building?

4. A cylindrical can is just big enough to hold three tennis balls. The radius of a tennis ball is 5 cm. What is the volume of air that surrounds the tennis balls?

You are part of a panel of parents, teachers, and administrators working to revise the geometry curriculum for the local high school. On tonight's agenda, you will be brainstorming creative ways to teach surface area and volume. The teachers are especially interested in methods which will help the students connect geometry to life in the "real world" because student motivation has sometimes been lacking in this course. What suggestions do you make to the panel during your discussion? Why do you think students would benefit from this idea being used in the classroom? Explain your idea in at least two paragraphs.

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Solution Summary

This problem set has five questions. The first four questions involve right triangles, circles, areas, volumes, perimeters, etc. The last question is a discussion question about using "real-world" methods to teach geometry.

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The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, as shown in the diagram below.

.Solve the following problems in a Word document.
1. A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including base and the center pole are to be made of aluminum tubing. How many feet of tubing should the team buy? How many square feet of the backstop must be covered by a screen?

To find out how much tubing to buy, we need to find out the length of the hypotenuse of the triangle. But, first, let's put all the measurements in feet:
24'8" = 24 + 8/12 feet = 24.6667 feet
6.5 yards = 6.5 * 3 feet = 19.5 feet
To find the hypotenuse of a triangle with sides 24.6667 and 19.5 feet, set up the following equation and solve for c:
C2 = (24.6667)2 + (19.5)2
C2 = 988.969
C = 31.448 feet
The total amount of tubing is 2(31.448) + 2(24.6667) + 19.5 = 131.729 feet
To find out how much screen we need, we have to find the area of the triangle:
A = ½ * height * base = (1/2)(19.5)(24.6667) = 240.5
Since there are two triangles, the ...

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