perplexus.info :: Shapes : The right pentagon

The right pentagon (Posted on 2004-06-12)

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
answer	K Sengupta	2008-07-11 11:54:09
Pai da ma	vije	2004-07-10 10:50:30
Solution	Gromit	2004-06-25 01:23:15
Solution	Tristan	2004-06-13 13:20:26
observation	rixar	2004-06-13 12:16:30
Solution	Nick Hobson	2004-06-13 10:26:15
Drawing	Tristan	2004-06-12 12:33:16
And the answer is ....	Larry	2004-06-12 12:30:42
OH...	Larry	2004-06-12 11:58:56
re: C is 90 and concave? - yes	Tristan	2004-06-12 11:54:16
C is 90 and concave?	Larry	2004-06-12 11:30:44

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