GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Quadrilateral PQRS has PQ = QR = RS = 5, If angle R = 90° and angle Q
[#permalink]
29 Mar 2021, 05:30
29 Mar 2021, 05:30
2
Expert Reply
3
Bookmarks
00:00
Question Stats:
71% (01:58) correct
28% (03:08) wrong based on 7 sessions
Hide Show timer Statistics
Quadrilateral PQRS has PQ = QR = RS = 5, If angle R = 90° and angle Q = 135° what is the area of the quadrilateral?
A. \(\frac{25 + \sqrt{2}}{2}\)
B. \(\frac{1 + 25\sqrt{2}}{2}\)
C. \(\frac{25(1 + \sqrt{2})}{2}\)
D. \(25 + \sqrt{2}\)
E. \(25 + 25\sqrt{2}\)
A. \(\frac{25 + \sqrt{2}}{2}\)
B. \(\frac{1 + 25\sqrt{2}}{2}\)
C. \(\frac{25(1 + \sqrt{2})}{2}\)
D. \(25 + \sqrt{2}\)
E. \(25 + 25\sqrt{2}\)
Re: Quadrilateral PQRS has PQ = QR = RS = 5, If angle R = 90° and angle Q
[#permalink]
29 Mar 2021, 23:03
29 Mar 2021, 23:03
4
1
Bookmarks
GeminiHeat wrote:
Quadrilateral PQRS has PQ = QR = RS = 5, If angle R = 90° and angle Q = 135° what is the area of the quadrilateral?
I can not share the figure with you since I am a new member in this forum and by its rule, I need to post at least 10 times before I can share. So, let me explain this verbally. Draw a figure. Join SP. Assume two triangles - triangle QRS and PQS.
In triangle QRS, angle R = 90, and QR = RS = 5. So \(area of triangle QRS = (1/2)*5*5\). Also, notice angle SQR = angle RSQ = 45, since it is a right isosceles triangle. Moreover, QS = 5\sqrt{2} by applying Pythagoras ratios in such a triangle.
In triangle PQS, angle PQS = 90, since 45° angle SQR is excluded from 135° angle PQR. Now PQ = 5, and QS = 5\sqrt{2}. So \(area of triangle PQS = (1/2)* 5 * 5\sqrt{2}\)
Add the areas of both triangle QRS and PQS.
C is the correct answer.
gmatclubot
Re: Quadrilateral PQRS has PQ = QR = RS = 5, If angle R = 90° and angle Q [#permalink]
29 Mar 2021, 23:03
Moderators:
