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In the figure above, all triangles have the same area. If the area of

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In the figure above, all triangles have the same area. If the area of [#permalink]

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New post 11 Nov 2017, 06:57
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In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

[Reveal] Spoiler:
Attachment:
2017-11-11_1745_002.png
2017-11-11_1745_002.png [ 53.1 KiB | Viewed 204 times ]


The OA will be automatically revealed on Saturday 18th of November 2017 05:57:25 AM Pacific Time Zone
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Kudos [?]: 132495 [0], given: 12323

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In the figure above, all triangles have the same area. If the area of [#permalink]

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New post 11 Nov 2017, 07:55
Bunuel wrote:
Image
In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

[Reveal] Spoiler:
Attachment:
2017-11-11_1745_002.png

The area of the shaded region is the area of the square minus 4 of the 8 triangles with the same area. So

The (area of the shaded region) equals the (area of the square) minus (\(\frac{1}{2}\) the area of all the congruent triangles), \(\frac{1}{2}T\):
\(84 = 100 - \frac{1}{2}T\)
\(\frac{1}{2}T = (100 - 84) = 16\)

The area enclosed by the thick outline equals the square plus \(\frac{1}{2}\) the area of the all the triangles:
Area = \(100 + \frac{1}{2}T\)
\(\frac{1}{2}T = 16\)

Area enclosed by thick outline = \(100 + 16 = 116\)

Answer D

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Re: In the figure above, all triangles have the same area. If the area of [#permalink]

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New post 11 Nov 2017, 08:02
Bunuel wrote:
Image
In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

[Reveal] Spoiler:
Attachment:
2017-11-11_1745_002.png


Area of shaded region + Area of 4 Triangles = Area of the square

So, 84 + Area of 4 Triangles = 100

So, Area of 4 Triangles = 100 - 84

Or, Area of 4 Triangles = 16

Since, Area of each triangle = 4

Since all the triangles are of equal area , the area of the total figure = Area of the square + area of 4 trinagles

Or, Area of the total figure = 100 + 16

Or, Area of the total figure = 116, answer will be (D)

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Kudos [?]: 1114 [0], given: 327

Re: In the figure above, all triangles have the same area. If the area of   [#permalink] 11 Nov 2017, 08:02
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In the figure above, all triangles have the same area. If the area of

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