Question

Here is your question do it fast

Answer 1

in triangle apqand abc angle p=<b and <q=<c (alternate interior )so by aa similarty crateria triangle apq similar to tri abc now ar(APQ)/ar(ABC)=AP/ABka hole square ,so its equal to (1/3)2=1/6

Answer 2

hey mate!!

in triangle apq and troangle abc
angle p= angle b (corresponding angles)
angle a =angle a (common)

by aa similarity rule triangle apq is similar to triangle abc

and ar(apq)÷ar(abc)=ap^2÷ab^2

given that ap/pb=1÷2
so, 2ap=pb

ab=ap+pb
ab=ap+2ap
ab=3ap

now, ar(apq)÷ar(abc)=ap^2÷(3ap)^2
=ap^2÷9ap^2
=1÷9=1:9

hence the ratio of ar(apq) and ar(abc) is 1:9

hope it helped!!