BdMO Problem 3
Geometry
Level
2
In rectangle ABCD, Q is a point located inside in such a way that PQ is perpendicular to AB and P point is on AB. Rectangle ABCD is divided into two regions, APQCD and PBCQ of equal area. If PB = 4,AD = 8 and PQ = 3,what is the area of ABCD?
The answer is 44.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Area of trapezium PBCQ = 1/2 x (PQ + BC) x PB = 1/2 x (3 + 8) x 4 = 22 ( Bcoz BC = AD in rectangle ABCD)
Also given, Ar(APQCB) = Ar(PBCQ)
So, Ar(ABCD) = Ar(APQCB) + Ar(PBCQ) = 22 + 22 = 44