Corner Cube Prism

Geometry Help!?

A square prism measures 1in on each side. the corner of the cube is cut off. The cut begins at the diagonal of each of the three squares on the prism. What is the area of the cut off corner?
(Show all work)

First, draw the picture.

Let me restate that.

First, DRAW THE PICTURE.

This should ALWAYS be the first step in problems like these.

Once you draw the picture, you will see the solution is quite obvious. You just have a triangle with each side equal to the diagonal length. By the Pythagorean Theorem, you know that the diagonal length is 1/√2, so you have an equilateral triange with each side length equal to 1/√2.

The formula for the area of a triangle is (1/2)bh. You know the base length to be 1/√2: Can you find the height? (Hint: If you draw a line from the top of the equilateral triangle right down to the base, that line is the height. It divides the triangle into two identical, mirror-image right triangles, each of which has a hypotenuse of 1/√2 and a base leg length of half that. You can use Pythagoras again to find the height.)

Short of actually plugging the numbers in for you, that's about as much help as I know how to give. Good luck.

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30-inch Corner Cube - Honey $51.99 The 9-in-1 Storage System delivers a quick and easy way to get organized. Use this piece horizontally or vertically!  The Corner Cube is made on a solid wood frame overlaid with MDF (medium density fiberboard) and pre-finished wood grain veneer that gives it a real furniture look and guards against moisture and scratches for long life. It is lightweight for quick, easy assembly and installation with an innovative hollow-core construction that weighs 50% less than traditional particle board. A strong MDF back is recessed, fitting perfectly into the four sides of the unit. Also features holes and dowels for sturdy stacking. Includes matching plugs for finishing the dowel holes. The Cube can hold 200 lbs. It offers unlimited combinations of set-up, great for the office, home, closet, kitchen, or any living area. The Corner Cube goes with other 9-in-1 pieces. This item ships directly from the manufacturer. Product usually arrives in 2-8 business days, depending on destination, including order processing and shipping. APO/FPO shipping unavailable

30-inch Corner Cube - White $51.99 The 9-in-1 Storage System delivers a quick and easy way to get organized. Use this piece horizontally or vertically!  The Corner Cube is made on a solid wood frame overlaid with MDF (medium density fiberboard) and pre-finished wood grain veneer that gives it a real furniture look and guards against moisture and scratches for long life. It is lightweight for quick, easy assembly and installation with an innovative hollow-core construction that weighs 50% less than traditional particle board. A strong MDF back is recessed, fitting perfectly into the four sides of the unit. Also features holes and dowels for sturdy stacking. Includes matching plugs for finishing the dowel holes. The Cube can hold 200 lbs. It offers unlimited combinations of set-up, great for the office, home, closet, kitchen, or any living area. The Corner Cube goes with other 9-in-1 pieces. This item ships directly from the manufacturer. Product usually arrives in 2-8 business days, depending on destination, including order processing and shipping. APO/FPO shipping unavailable

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30-inch Corner Cube - Honey - by Foremost $63.65 The 9-in-1 Storage System features a rich honey finish and delivers a quick and easy way to get organized. Use this piece horizontally or vertically! The Corner Cube is made on a solid wood frame overlaid with MDF (medium density fiberboard) and pre-finished wood grain veneer that gives it a real furniture look and guards against moisture and scratches for long life. It is lightweight for quick, easy assembly and installation with an innovative hollow-core construction that weighs 50% less than traditional particle board. A strong MDF back is recessed, fitting perfectly into the four sides of the unit. Also features holes and dowels for sturdy stacking. Includes matching plugs for finishing the dowel holes. The Cube can hold 200 lbs. It offers unlimited combinations of set-up, great for the office, home, closet, kitchen, or any living area. The Corner Cube goes with other 9-in-1 pieces. Type: Storage Accessories Color: Yellow

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My Solved Octagonal Prism Rubik's Cube

Who invented PRISM RETOROREFLECTORS and in what year?

Prism retororeflectors are also called corner cube prisms. Prism retororeflectors have three internal reflections, with these can reflect it back onto itself — regardless of the prism’s orientation.

Inventors: Rowland, William P.; Nilsen, Robert B.
From here:

http://www.eipa-patents.org/Lighting/Find-patent-Miniature-micro-prism-retroreflector-570107.htm

From This Google Search:
[invention of PRISM RETROREFLECTORS]

http://www.google.com/search?hl=en&rlz=1R2GGLL_en&ei=u9oFSp7MJZyatAPt66DtAQ&sa=X&oi=spell&resnum=1&ct=result&cd=1&q=invention+of+PRISM+RETROREFLECTORS&spell=1

Hope this helps.
Wingman