If AB = BC, which of the following is an expression for the area of qu

Question

https://gmatclub.com/forum/download/file.php?id=41444 If AB = BC, which of the following is an expression for the area of quadrilateral ABDE ? A) \frac{a^2}{2} - \frac{b^2}{2} B) \frac{a^2}{2} + \frac{b^2}{2} C) a^2 - b^2 D) \frac{a^2}{4} - \frac{ab}{2} E) \frac{a^2}{4} + \frac{ab}{2} KBX8gdr.jpg

gmatlover12 · Answer

The trick here is to understand that riangle ABC is an isoceles right triangle, AND riangle EDC is also isoceles right triangle If you need to understand this in detail, use this link: https://proofwiki.org/wiki/Parallel_Lin ... ortionally riangle ABC - riangle EDC = required area of quadrilateral = { \frac{1}{2} x a x a} - { \frac{1}{2} x b x b} Thus, option A

sumitkrocks · Answer

AB=BC ...Or Triangle ABC is an isosceles triangle , equal side make equal angle on common base ...so Angle BAC and angle BCA=45

from above we can infer angle DEC will be 45 degree , so DE=DC=b 
Hence , BD=BC-CD=a-b

Angle of quadrilateral , please note angle ABC and CDE are 90 degrees and hence Line AB and DE must be parallel ..We can infer Quad BDEA is a trapezium 
Area of trapezium =1/2*Sum of parallel sides*distance b/w them

1/2*(Length of AB+ length of DE)*length of BD
=1/2*(a+b)*(a-b)
=1/2(a^2-b^2) Answer A

Alternately , we can calculate area of Triangle ABC and triangle CDE and subtract to get area of Quad ABDE directly 
i.e 1/2 (a*a-b*b)

Hope it helps

PP777 · Answer

Given: AB = BC = a ; angle ABC = 90 ; angle EDC = 90
To find: Area of quadrilateral ABDE

Approach: Area of quadrilateral ABDE = Area of triangle ABC - Area of triangle EDC
 
We know that AB=BC and ABC = 90, therefore angle ACB = angle BAC = 45
So,Area of isosceles right-angled triangle ABC= (1/2) * AB * BC = (1/2) a * a = (a^2)/2 ........................................................1

In triangle EDC, ED= b angle EDC = 90 and angle ACB= 45
therefore angle DEC= 45
so, triangle EDC is an isosceles right-angled triangle.
=> ED = CD = b

Area of isosceles triangle EDC = (1/2)* ED * CD = (1/2) * b * b = (b^2)/2...........................................................2

Therefore, Area of quadrilateral ABDE = Area of triangle ABC - Area of triangle EDC = (a^2)/2 - (b^2)/2

Correct Answer =A

CAMANISHPARMAR · Answer

riangle ABC , and  	riangle EDC are similar triangles in multiple ways.

Hence if  	riangle ABC is an isoceles right triangle, then  	riangle EDC is a similar triangle hence is also isoceles right triangle.

For  	riangle ABC : AB = BC = a

Then for  	riangle EDC : ED = DC = b

Area of  	riangle  ABC - Area of  	riangle  EDC = Area of quadrilateral ABDE

Area of quadrilateral ABDE = { \frac{a^2}{2} } - { \frac{b^2}{2} }

Therefore the correct answer is A

ScottTargetTestPrep · Answer

We see that the area of quadrilateral ABDE is the difference between the areas of triangle ABC and triangle EDC.

Since AB = BC and angle ABC is a right angle, triangle ABC is an isosceles right triangle.

Because two of their interior angles are equal, triangles ABC and EDC are similar. So triangle EDC is also an isosceles right triangle.

Thus the area of triangle ABC = (1/2)(a)(a) = a^2/2 and the area of triangle EDC = (1/2)(b)(b) = b^2/2.

Thus, the area of quadrilateral ABDE is:

a^2/2 - b^2/2

Answer: A

If AB = BC, which of the following is an expression for the area of qu

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If AB = BC, which of the following is an expression for the area of qu

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards