Pranav N.

asked • 02/17/15

find the are of pentagon ABCDE

DP is drawn perpendicular to AB and is also perpendicular to CE at point Q. if AP = BP = 12cm, EQ = CQ = 8cm, DE = DC = 10cm and DP = 18cm 

Philip P.

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Where are points P and Q?
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02/17/15

Matt H.

I think the question implies that P is the midpoint of AB (picture along the bottom of the pentagon), and Q is the midpoint of CE (a horizontal segment parallel to the bottom).
 
But I think then it gets weird, because the lengths don't work. The way I am visualizing the shape, AP and BP would have to be shorter than CQ and EQ, but the numbers say otherwise.
 
Anyway, Pranav, one of your keys here is to assume that this is a regular pentagon, which means all the sides are congruent. We know that 2 of them measure 10 cm, so they all do. Perhaps you can subdivide the shape into triangles and go from there?
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02/17/15

1 Expert Answer

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Barbara H. answered • 02/17/15

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a^2 + b^2 = c^2   a^2 + 8^2 = 10^2     a^2 = 10^2 - 8^2   a^2 = 36    a = 6cm.  
 
Since there are two triangles  that measure 6cm. and 8cm., their area together would be 6 x 8 = 48 cm.^2
 
There are two rectangles that measure 12cm. x 8 cm.= 192cm.^2
 
There are two triangles at the base that measure 4 x 12 = 48cm.^2
 
48 + 48 + 192 = 288cm.^2
 
 
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