A quadrilateral has a perimeter of 16. What is the area of the quadril

Question

A quadrilateral has a perimeter of 16. What is the area of the quadrilateral?

(1) The width is 40% of the length
(2) All angles are of equal measure

Archit3110 · Answer

quadrilaterl can be square , rhombus or a rectangle or ∆ 
#1

insufficient ; but we dont know whether figure is ∆ or a rectangle or any other shape quadrilateral 
#2
all angles are same ; so we cannot determine anything in specific insufficient 
from 1 & 2
sides are equal measure and given info about l & w ; we can say that its a rectangle
so 
let l = x so w = 0.6x
given x+x+0.6x+0.6x=16
x= 5 ; l and w = 3
area = 15
IMO C

chetan2u · Answer

Quadrilateral can be of any shape..
You are confusing the two terms quadrilateral and parallelogram.

VeritasPrepBrian · Answer

+1 to what Chetan said *and* I'll add - if you don't know statement 2, that you're dealing with all 90-degree angles and thus a rectangle, then your multiplying the length times the width isn't necessarily how you'd find the area. If you don't have 90-degree angles (a square or rectangle) then you have to multiply base times height, where the height is perpendicular to the base. That distance in other parallelograms is different from the side (you generally have to form a right triangle to calculate that perpendicular height). So statement 1 isn't sufficient: 3 * 5 = 15 is one possible area, but if the shape is a non-rectangle then it would be 5 * h and h would not be 3.

A strategic note here - this is a great example of a strategy we teach at Veritas Prep called "Why Are You Here?" Statement 2 is pretty clearly insufficient on its own, but if you liked Statement 1 by assuming you had a rectangle and then see statement 2 specifically telling you that you have a rectangle (4 equal angles), you should consider "hey do I need them to tell me that or do I already know that?" To me that's an invitation to redraw the shape with something *other* than 90-degree angles and that should show you that a parallelogram is possible.

Archit3110 · Answer

thanks a lot

VeritasPrepBrian & chetan2u for the explanation, I now understand where I went wrong...

pulak1988 · Answer

I don't under stand.

statement 1: it says the quad has length and width. so no matter what the shape of quad is, the perimeter will 2( L + W). right?

LeoN88 · Answer

Given Quadrilateral- A closed figure with four sides- can be square, rectangle or parallelogram, rhombus etc.
Let's start with easy statement 2.

Equal measure of angles can be a square/rectangle we don't know. So insufficient.

Statement 1.
L=100x, w=40x, but again it can be any rectangle, kite etc. we don't know.

1+2: Definitely a rectangle-> Find x and then find the area.  (C)

LeoN88 · Answer

pulak1988

True, if it's a parallelogram then the area would be= h*base
For rectangle, area= width*height; in different cases we are getting different areas.

Check GMAT Book page 69

prabsahi · Answer

I guess you are assuming the shape as a rectangle and so assuming the formula as 2( L + W). From statement 1 its clearly not clear what is the shape 
of the quadrilateral .(It can be rectangle/square/rhombus/trapezoid/or any other quad with all four sides different.)

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A quadrilateral has a perimeter of 16. What is the area of the quadril

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A quadrilateral has a perimeter of 16. What is the area of the quadril

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