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Browse High School Practical Geometry

Stars indicate particularly interesting answers or good places to begin browsing.



Carrying a Ladder around a Corner [02/28/2003]
A ladder of length L is carried horizontally around a corner from a hall 3 feet wide into a hall 4 feet wide. What is the length of the ladder?

Frustum of a Cone [12/09/1996]
If you cut a cone and then lay it out on a flat surface, what will be the inside and outside sizes of this flattened-out cone?

Jobs That Use Geometry [12/18/2001]
I would like to learn how geometry is used in real life. What jobs involve geometry?

Modeling How Much Wood Expands [09/21/2013]
A flooring inspector seeks to quantify how much wood buckles as it expands. Drawing on trigonometric approximations, Doctors Rick and Peterson each provide heuristics for this real world problem.

Real-World Carpentry and Trigonometry [11/19/2002]
I'm trying to come up with a formula to calculate the height of an arc at the midpoint of the chord that defines it knowing only the length of the arc and the length of the chord.

Three Tapers and a Length [8/25/1995]
I have three tapers (or angles) that intersect with each other. Theoretically, if I were given the total length from 0 to Y and the total height 0 to X and of course the three angles, is it possible to calculate each angles length and height?

Two Crossing Ladders [07/01/2003]
Two walls are 10 ft. apart. Two ladders, one 15 ft. long and one 20 ft. long, are placed at the bottoms of the walls leaning against the opposite walls. How far from the ground is the point of intersection?

Accurate Drawing of an Ellipse [02/14/1999]
Draw an ellipse accurately using simple tools.

A-frame for Swing [07/26/1997]
I am trying to build a stand for a swing. The ends are A-frames out of 4 by 4's... what is the angle of the miter cut?

Angle Between Two Sides of a Pyramid [10/29/1999]
How can I compute the angle formed by two sides of a frustrum of a pyramid?

The Angles of a Roof [11/20/1995]
I am trying to build a model house but am having trouble with laying out the roof. The main part of the house has a peaked roof (an "A" frame house); the angle formed when the roof meets the ground is 60 degrees. There is an addition onto the A-frame with a 30 degree angle formed to the walls. What angle should the addition's roof be cut at so it meets the A-frame roof?

Applications of Parabolas [10/24/2000]
How are parabolas used in real life?

Area of a Lawn [09/04/2002]
I have two areas of lawn that I want to sod with new grass and don't know how much sod to buy.

Area of an Unusual Hexagon [12/05/1996]
Find the area of a hexagon made from a triangle with squares appended to each of its sides and three more triangles each consisting of one unknown side and two sides which are shared with two of the squares.

Areas of House Lots [02/18/1998]
We have to determine sanitary sewer assessments of properties based on the square feet of their lots. Many lots are 4-sided but do not have any parallel lines...

Azimuth Angle [09/08/1998]
Can you give me the formula for the azimuth angle and explain some of the terminology?

Board Feet from a Log [03/19/2003]
What is the board feet of a 10-foot log if the diameter is 16 inches at one end and 14 inches at the other end?

Bricks to Cover a Steeple [08/23/1997]
How many 6"x12" bricks would it take to cover an octagonal steeple with a diameter of 130 ft. and a height of 370 ft?

Building a Circular Horse Pen [06/16/2002]
My Dad and I are building a round pen for our horse. We have 16 16ft. panels and a 10 ft. gate and a 4ft. gate. (270 ft. total) We want to use a radius and mark the places to dig holes for each post that will support the panels, but we don't know how long the radius should be. Can you help?

Building a Cone [10/28/2001]
I am trying to find a formula for building a cone for a chimney flashing. It should be 21" tall with a top opening of 8", a bottom opening of 20", and a vertical seam overlap of 2".

Building a Manger [12/03/2001]
Given a base of 11" and two walls 7 1/2' and 6" high, both meeting the base a 90-degree angles, what is the length of the roof and what are the angle measures where the walls meet the roof?

Building a Skateboard Ramp [9/19/1995]
I'm trying to build a skateboard ramp, pyramid with flat top, height one foot, angle of ascent thirty degrees, other angles ninety degrees and sixty degrees.

Building a Wooden Square-Based Pyramid [01/26/2001]
I want to build a wooden pyramid with a square base 8"by 8".

Calculating Areas of Quadrilaterals and Triangles [08/30/2005]
What portion of an acre is a plot of land that is 85 x 174 x 73 x 118? How about a plot of land that is 150 x 118 x 150?

Calculating How Much Paper Is on a Roll [04/24/2006]
How many feet of paper are on a roll of paper with a diameter of 48" if the core has a diameter of 4" and the paper is 0.014" thick?

Calculating Polygon Area [01/11/2004]
How can you determine the area of an unusually shaped polygon?

Calculating Square Footage or Area [01/08/2007]
In my job I am often asked to figure out square footage. What are the formulas to find the areas of rectangles, triangles, and odd shapes?

Calculating the Angle of a Plank [08/22/2001]
Are there any equations that could be used to solve for a plank of known width?

Calculating the Length of String on a Reel [12/07/2001]
Is there a formula for calculating the length of wire that can go on a reel (spindle) where the reels may have different diameters, hub diameters, and widths, and the wires may have different diameters?

Calculating the Square Footage of a House [04/01/2004]
Is there an exact formula for finding the square footage of a house?

Carpet and Room Areas [10/26/2001]
A man buys a roll of carpet 9 ft. wide by 12 ft. long to fit a 10ft. by 10 ft. room. When the roll of carpet is unrolled, a hole is discovered in the middle of the carpet...

Carpet Problem [10/15/2001]
You have to carpet a 9x12 room, but when you go the store they only have a 10x10 carpet and a 1x8 piece of carpet...

Centering Circles [10/05/2002]
Two metal disks need to be centered on each other, but the circle with the larger diameter has the center cut out. How can you center them by knowing the diameters?

Chords From Inscribed Polygons [07/11/2002]
An regular polygon is inscribed in a circle of known radius. Each side of the octagon is a chord of the circle. What is the length of each chord?

Civil Engineering and Math [02/25/1997]
What forms of math or physics do civil engineers commonly use?

Coin With 11 Sides and a Constant Diameter [10/20/2007]
I was told that one of the reasons why a Canadian Loonie coin is 11-sided is that it rolls better than a 10-sided coin. Why is that?

Constructing a Pyramid [05/28/1999]
How can I calculate the sides and angles needed to construct a pyramid with an 8-foot-square base and a height of 6 feet?

Constructing a Sphere out of Paper [02/08/2003]
I'm working on a school project and can't seem to find the answer anywhere. The assignment is to construct a 3D 9'-diameter sphere out of paper.

Coordinate Systems, Longitude, Latitude [04/19/1997]
Can you explain pitch, roll, and yaw to me? Are there other systems for measuring an object's position in space?

Cross-Cornering a Shape to Make it Square [12/19/2002]
We lay out a building that is 30' x 40' and cross-corner it to see if it is 'square,' but there is a 6' difference. What is the equation to find how far to move one side to make the shape 'square'?

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