geometry

Question

What is the area of the shaded quadrilateral in the figure above?

(1) a^2−b^2=40

(2) a^2+b^2=58

animesh mohanty · Answer

statement 1 does not lead to any solution as we need the length of one of the sides of the shaded region.

Statement 2 on the other hand directly gives us the square of length the side.
 a^{2}    + b^{2}   = 58 since all sides are equal the given info is sufficient.

Sasindran · Answer

Please be elaborate

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kunalsinghNS · Answer

The given figure is a square since each side is a+b. Hence, area of a square is (a+b)^2

We get 4 triangles if we cut out the quadrilateral from the given square. Since, each triangle is a right angle and we know that the area of a right angle triangle is 1/2 * (Base)* (Height).
So area of 4 triangles in terms of a and b = 2ab

Hence area of the quadilateral = area of the square - area of 4 trianlges
 a^2+b^2+2ab - 2ab

hence area is a^2 + b^2

1) a^2 - b^2 = 40, Insufficient

2) a^2 + b^2 = 58, Sufficient

Answer B

animesh mohanty · Answer

statement 2 tells us a^2+b^2 =58
by using pythagorean theorem we find out that the length any of the sides of the shaded region is  \sqrt{58}

Bunuel · Answer

Discussed here: what-is-the-area-of-the-shaded-quadrilateral-in-the-figure-above-234988.html Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html TOPIC IS LOCKED AND ARCHIVED.

geometry

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