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.
The points of a six-pointed star consist of six identical equilateral
[#permalink]
02 Feb 2023, 04:28
02 Feb 2023, 04:28
Expert Reply
1
Bookmarks
00:00
Question Stats:
100% (01:11) correct
0% (00:00) wrong based on 6 sessions
Hide Show timer Statistics
Attachment:
GRE The points of a six-pointed.jpg [ 11.88 KiB | Viewed 1056 times ]
The points of a six-pointed star consist of six identical equilateral triangles, with each side 4 cm (see figure). What is the area of the entire star, including the center?
Show: ::
\(48 \sqrt{3}\)
Re: The points of a six-pointed star consist of six identical equilateral
[#permalink]
18 Feb 2023, 02:50
18 Feb 2023, 02:50
Expert Reply
OE
Think of this star as a large equilateral triangle with sides 12 centimeters long, and three additional smaller equilateral triangles (shaded in the figure below) with sides 4 inches long. Using the same 30–60–90 logic you applied in problem 9, you can see that the height of the larger equilateral triangle is
\(6 \sqrt{3}\)
and the height of the smaller equilateral triangle is \(2 \sqrt{3}\)
The area of the large triangle is \(36 \sqrt{3}\)
The small ones are \(4 \sqrt{3}\)
The sum of both is \(48 \sqrt{3}\)
Think of this star as a large equilateral triangle with sides 12 centimeters long, and three additional smaller equilateral triangles (shaded in the figure below) with sides 4 inches long. Using the same 30–60–90 logic you applied in problem 9, you can see that the height of the larger equilateral triangle is
\(6 \sqrt{3}\)
and the height of the smaller equilateral triangle is \(2 \sqrt{3}\)
The area of the large triangle is \(36 \sqrt{3}\)
The small ones are \(4 \sqrt{3}\)
The sum of both is \(48 \sqrt{3}\)
gmatclubot
Re: The points of a six-pointed star consist of six identical equilateral [#permalink]
18 Feb 2023, 02:50
Moderators:
