Data Sufficiency

Could someone help me with this one please ?

ABCD is a quadrilateral. A rhombus is a quadrilateral whose sides are all congruent. BCEF is a
rhombus and shares a common side with the quadrilateral ABCD. The area of which one is greater:
ABCD or BCEF ?
(1) ABCD is a square.
(2) BCEF is not a square.

OA C

TOugh one to explain.

A square that shares the same side length with a rhombus will be larger than the rhombus.

Just cannot figure out how to explain this.

hi guys let me try
(1) if abcd is square that shares the the side with rhombus bcef then they have equal sides say-x
and the area of square=x^2,
the area of rombus will=x^2*sin(b) where sinb is the value of angle formed by the sides od rombus
if sin(b)=1 (sin90=1) then their areas are equal x^2*1=x^2
sin can`t be greater that 1, so if angle between sides of rombus is less than 90. sin will be less then 1 and product of x^2*(value less that 1)will be <then simple x^2
but we are not given any property of rombus
and 1 st insuff
(2)rombus is not a square, it happens that the area of rombus=x^2*sinb, and sinb<1
but we have no info about abcd
both
area of rombus=x^2*sinb, where sinb<1
area of square=x^2
clearly that area of square is greater then that of rombus
both suff
i agree this is hard one problem

Let me try to explain this without heavy math involved.

now ABCD is a quadrilateral. BCEF is a rhombus. both share common side BC. ABCD can be anythng-sqare,rhombus,rectangle.
now stat1: abcd is sqauare. so area=x^2 (assuming x is the side) so the rhombus too has all sides as x. area of rhombus can alo be expresses as b*h where b is one side (As all sides are equal) h is the height.here b=x
now we need to knw whether x^2 is greater than or less than x*h. how to find the height of rhombus?
u will need to draw the pic to get this better. the opp sides in a rhombus are parallel.
once u draw a perpendicular from one side to the other, you can see a right triangle with one of the sides as hypotenuse.
so whtevr the measurement of the height it WILL be less than the hypotenuse. so h is always less than b. this i enough to say that area of square is >area of rhombus
BUT
stat1 just says that BCEF is a rhombus. square is also a type of rhombu, in which case both areas will eb equal.
so we need stat 2 also which confirms it is not the case.

using 1 & 2 its clear than area of ABCD is more.
main point here is to establish for a given side area of square is > area of rhombus

hope im not missing anythgn here in my explanation

This question can be very easily solved with a property of a quadilateral:-

A square has a larger area than any other quadrilateral with the same perimeter

Now for (1) ABCD is a square, but we know nothing about BCEF. Another property is

If the diagonals of a rhombus are equal, then that rhombus must be a square. Now as we see,

we only know that BCEF is a Rhombus, we know nothing about the angle. Hence (1) insufficient.

(2) Insufficient

(1) + (2), here we get that BCEF is not a square, hence clearly Area ABCD > Area BCEF Sufficient

Hence C