Solve the below question:-
Q.In the adjoining figure ABCDEFGH is an octagon comprising of 16 congruent rectangles of size 4 x 1 each. 
P is a point on EF such that AP divides the octagon into two parts of equal areas. 
Find the length of AP. 

Dear student

Area of this octagon= 16 x area of 1 rectangle
                                 = 16 x 4 x 1= 64 square units
AP divides this figure into two equal parts so 
area of one half= 32 square units   

area of APFGHQ(one half)= area of triangle APQ + area of rectangle FGHQ(on observing the figure)
Area of rectangle FGHQ= 2 x 4 x 1= 8 square units
(it has two rectangle out of 16)
so area of triangle APQ= 32-8= 24 sq. u.
Area of triangle APQ(as we know)=
12× Base × Height24=12×8×PQPQ=24×28=6 units
As APQ is a right angled triangle with base AQ= 8 unit and PQ= 6 unit
AP forms the hypotenuse of triangle
So
AP2=AQ2+PQ2      = 82 + 62      = 64+36=100=102So AP=10 units
Regards

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