Geometry Word Problems
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Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. 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.
The problems in this Unit will give you an opportunity to practice these applications.
Solve the following problems and submit them 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?
5. 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
Geometry word problems are solved.
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To start off geometry questions I find it helpful to spend some time visualising the (possibly) 3D structure described in the question until you can clearly see it in your minds eye.
Next try to identify all the key equations that you know can be applied to those structures.
Finally plug in the appropriate values for the variables into your equations to get the required answers.
Lets apply this to the four questions:
1. Visualise the two right angled triangles joined along one side. Visualise that we need five of those aluminium pipes - and we are given the lengths for all but two of them (which happen to be the hypotenuse of the right angled triangles). The area of screen is going to be the sum of the areas of the two triangles.
To find the length of piping needed:
c^2 = a^2 + b^2 - Pythagoras ( c^2 meaning c squared or c to the power 2)
Where c is the hypotenuse (our unknown pipe length)
a is the length of the pipe along the ground = 24' 8'' = 296''
b is the length of ...
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