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Difficulty:
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Question Stats:
80% (01:24) correct
20%
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wrong
based on 169
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What is the area of the shaded quadrilateral in the figure above?
(1) a^2 − b^2 = 40
(2) a^2 + b^2 = 58
Attachment:
shadedQuad.png [ 11.99 KiB | Viewed 5937 times ]
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CareerGeek
Joined: 20 Jul 2017
Last visit: 06 Sep 2026
Posts: 1,285
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
GMAT 1: 690 Q51 V30
Posts: 1,285
Bunuel
We can see that all the sides of the shaded quadrilateral are same and are the hypotenuse of a right angled triangle with sides a & b
--> The shaded quadrilateral is a square or rhombus.
Also, note that the diagonals of the shaded quadrilateral are equal
--> We can conclude that shaded quadrilateral is a square
--> Side of the square = \(\sqrt{a^2 + b^2}\)
Area of the shaded square = \(side^2 = a^2 + b^2\)
(1) a^2 − b^2 = 40
--> Insufficient
(2) a^2 + b^2 = 58
--> Area = 58
--> Sufficient
Option B
Posts: 217
Using Pythagoras Theorem:
All the sides of the shaded quadrilateral are equivalent (it is a square) and equal to \(\sqrt{a^2 + b^2}\)
Area of square = \(side^2\) = \((\sqrt{a^2 + b^2})^2\) = \(a^2 + b^2\)
Statement 1:
\(a^2 - b^2 = 40\)
From above statement we cannot get value of \(a^2 + b^2\).
Area is still unknown.
Statement 1 is Not Sufficient.
Statement 2
\(a^2 + b^2 = 58\)
Area = \(a^2 + b^2\) = 58
Statement 2 is Sufficient.
So, correct answer is option B.
_________________
All the sides of the shaded quadrilateral are equivalent (it is a square) and equal to \(\sqrt{a^2 + b^2}\)
Area of square = \(side^2\) = \((\sqrt{a^2 + b^2})^2\) = \(a^2 + b^2\)
Statement 1:
\(a^2 - b^2 = 40\)
From above statement we cannot get value of \(a^2 + b^2\).
Area is still unknown.
Statement 1 is Not Sufficient.
Statement 2
\(a^2 + b^2 = 58\)
Area = \(a^2 + b^2\) = 58
Statement 2 is Sufficient.
So, correct answer is option B.
_________________
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