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655-705 (Hard)|   Geometry|      
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Bunuel
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Two equilateral triangles, each of area (√3), and three squares were Mon May 10, 2021 9:00 pm
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C
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55% (hard)

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57% (01:58) correct 43% (02:21) wrong based on 51 sessions

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Two equilateral triangles, each of area (√3), and three squares were combined to form the figure above. If this figure were to be cut out of paper and folded to form a prism of triangular base, what would be the volume of the prism?

A. 2
B. 3
C. 2√3
D. 4√3
E. 6

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C
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Bunuel
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Two equilateral triangles, each of area (√3), and three squares were Sun May 16, 2021 2:30 am
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Bunuel

Two equilateral triangles, each of area (√3), and three squares were combined to form the figure above. If this figure were to be cut out of paper and folded to form a prism of triangular base, what would be the volume of the prism?

A. 2
B. 3
C. 2√3
D. 4√3
E. 6

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The volume of a prism is (area of the base)*(height).

The area of equilateral triangle is \(side^2*\frac{\sqrt{3}}{4}\). Thus we have that \(side^2*\frac{\sqrt{3}}{4}=\sqrt{3}\) --> \(side=2\).

From the image given we can infer that the side of the triangles is also the side of the squares. Since the side of the square is the height of the prism, then the volume of the prism is (area of the base)*(height) = \(\sqrt{3}*2\).

Answer: C.

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JoyeetaChak
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Two equilateral triangles, each of area (√3), and three squares were Mon May 10, 2021 11:15 pm
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Given :

Area of equilateral triangle = (√3)

Considering each side of the triangle = a

Height of the prism here is √3a/2 <This is also the height of the equilateral triangle>


Therefore, 1/2*a*√3a/2 = √3
=> a^2 = 4
=> a = 2

Area of the base of the prism = a^2 = 4
Height of prism = √3


Volume of a triangular prism = Height of prism * area of the base
= √3 * 4

Answer : Volume = 4√3

IMO D
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Two equilateral triangles, each of area (√3), and three squares were Mon May 10, 2021 11:19 pm
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Bunuel

Two equilateral triangles, each of area (√3), and three squares were combined to form the figure above. If this figure were to be cut out of paper and folded to form a prism of triangular base, what would be the volume of the prism?

A. 2
B. 3
C. 2√3
D. 4√3
E. 6

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The volume of the triangular prism will be = Area of triangle*height

Area of triangle = \(\sqrt{3}\)

Area of an equilateral triangle = \(\frac{\sqrt{3}*a^2}{4}\)

So, \(\frac{\sqrt{3}*a^2}{4}=\sqrt{3}...............a^2=4....a=2\)

Now sides of triangle and square are same as they share a common side => a=height=2...The height of prism = side of the square

Volume = \(\sqrt{3}*2\)

C
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Two equilateral triangles, each of area (√3), and three squares were Mon May 10, 2021 11:24 pm
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JoyeetaChak
Given :

Area of equilateral triangle = (√3)

Considering each side of the triangle = a

Height of the prism here is √3a/2 <This is also the height of the equilateral triangle>


Therefore, 1/2*a*√3a/2 = √3
=> a^2 = 4
=> a = 2

Area of the base of the prism = a^2 = 4
Height of prism = √3


Volume of a triangular prism = Height of prism * area of the base
= √3 * 4

Answer : Volume = 4√3

IMO D
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By taking the base as square, you are looking at a cube/cuboid when you look for volume by multiplying by height.

Here the base will be triangle, and that is why it is called triangular prism.
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Two equilateral triangles, each of area (√3), and three squares were Tue May 11, 2021 7:13 am
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chetan2u
JoyeetaChak
Given :

Area of equilateral triangle = (√3)

Considering each side of the triangle = a

Height of the prism here is √3a/2 <This is also the height of the equilateral triangle>


Therefore, 1/2*a*√3a/2 = √3
=> a^2 = 4
=> a = 2

Area of the base of the prism = a^2 = 4
Height of prism = √3


Volume of a triangular prism = Height of prism * area of the base
= √3 * 4

Answer : Volume = 4√3

IMO D

By taking the base as square, you are looking at a cube/cuboid when you look for volume by multiplying by height.

Here the base will be triangle, and that is why it is called triangular prism.
Thank you for clarifying. Much appreciate it. My bad I missed the important aspect.[quote="chetan2u"]
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Two equilateral triangles, each of area (√3), and three squares were Wed May 12, 2021 12:08 pm
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JoyeetaChak
Given :

Area of equilateral triangle = (√3)

Considering each side of the triangle = a

Height of the prism here is √3a/2 <This is also the height of the equilateral triangle>


Therefore, 1/2*a*√3a/2 = √3
=> a^2 = 4
=> a = 2

Area of the base of the prism = a^2 = 4
Height of prism = √3


Volume of a triangular prism = Height of prism * area of the base
= √3 * 4

Answer : Volume = 4√3

IMO D
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Looks like you took it the other way, it should have been triangle as the base.
So by definition "the triangle base followed the surrounded three squares, and then covered by another eq. triangle"

makes the volume of the prism = Area of triangle * height
= (3)^1/2 * 2

Answer : C
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