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The right pentagon (Posted on 2004-06-12) Difficulty: 3 of 5
There is a pentagon ABCDE such that angles A, C, and E are all right angles and it is concave at angle C.

If a ray starting at D was aimed at C, it would go exactly 1 inch before going through C, and would eventually go through A.

If BC and AE are both 5 inches, what is the area of this pentagon?

  Submitted by Gamer    
Rating: 3.3333 (6 votes)
Solution: (Hide)
If diagonal DA is constructed, it can be seen that two triangles are formed. Then, it can be shown that these triangles are congruent because their angles and one side of each (BC and AE) are the same length.

To figure out AD and AB, an equation would need to be created.

AC^2 + BC^2 + AB^2
(AD-CD)^2 + 25 = AB^2
(AB-1)^2 + 25 = AB^2
AB^2-2AB+1+25=AB^2
26=2AB
AB=13

Then since AB = 13, AC must equal 12. Since 30 = 1/2 base x height, 30 = (AC x BC) /2, or (12 x 5)/2. Since there are two of these triangles, the total area is 60 square inches.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2008-07-11 11:54:09
SolutionPai da mavije2004-07-10 10:50:30
SolutionGromit2004-06-25 01:23:15
SolutionSolutionTristan2004-06-13 13:20:26
observationrixar2004-06-13 12:16:30
SolutionSolutionNick Hobson2004-06-13 10:26:15
Hints/TipsDrawingTristan2004-06-12 12:33:16
SolutionAnd the answer is ....Larry2004-06-12 12:30:42
Some ThoughtsOH...Larry2004-06-12 11:58:56
re: C is 90 and concave? - yesTristan2004-06-12 11:54:16
QuestionC is 90 and concave?Larry2004-06-12 11:30:44
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