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In the diagram, square ABCD has side length 3.  Find the area of triangle PDQ.

 

 Dec 20, 2023
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tan (angle ABP)  = AP/AB =  1 / 3

Angle ABP + angle BPA = 90

Angle DPQ + angle  BPA = 90

So angle ABP = angle DPQ

 

tan (ABP)  = tan ( DPQ)

1/3  = DQ / 2

DQ = 2/3

 

Area of PDQ =  (1/2) (PD)(DQ)  = (1/2)(2)(2/3)  =  2/3

 

cool cool cool

 Dec 20, 2023

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