BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

In the diagram, \(HJLM\) is a square, and \(GH = 10.\) Find the area of trapezoid \(GHJK.\)

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1622
Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members
by Gmat_mission » Sun Apr 26, 2020 12:06 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

gpp-sgf_img3.png
In the diagram, \(HJLM\) is a square, and \(GH = 10.\) Find the area of trapezoid \(GHJK.\)

A. \(50+25\sqrt3\)

B. \(50+50\sqrt3\)

C. \(75+12.5\sqrt3\)

D. \(75+25\sqrt3\)

E. \(75+50\sqrt3\)

[spoiler]OA=D[/spoiler]

Source: Magoosh
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8156
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: In the diagram, \(HJLM\) is a square, and \(GH = 10.\) Find the area of trapezoid \(GHJK.\)

by Scott@TargetTestPrep » Sun May 03, 2020 5:22 am
Gmat_mission wrote: ↑
Sun Apr 26, 2020 12:06 pm
 gpp-sgf_img3.png

In the diagram, \(HJLM\) is a square, and \(GH = 10.\) Find the area of trapezoid \(GHJK.\)

A. \(50+25\sqrt3\)

B. \(50+50\sqrt3\)

C. \(75+12.5\sqrt3\)

D. \(75+25\sqrt3\)

E. \(75+50\sqrt3\)

[spoiler]OA=D[/spoiler]

Source: Magoosh
We see that triangle GMH is a 30-60-90 right triangle and since GH = 10, we have GM = 10/2 = 5 and HM = 5√3 (notice that HM is the height of trapezoid GHJK).

Since HJLM is a square, HM = 5√3 means HJ = ML = 5√3 (notice that HJ is one of the bases of the trapezoid).

Since triangles GMH and KLJ are congruent, GM = KL = 5. Therefore, GK, the other base of the trapezoid, is 5 + 5√3 + 5 = 10 + 5√3.

Since the area of a trapezoid is ½ x (sum of the two bases) x height, the area of trapezoid GHJK is:

½ x (5√3 + 10 + 5√3) x 5√3 = ½ x (10 + 10√3) x 5√3 = ½ x (50√3 + 150) = 25√3 + 75

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1