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11 Nov 2017, 06:57
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
87% (01:16) correct
13%
(01:05)
wrong
based on 77
sessions
History
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Not Attempted Yet
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
Attachment:
2017-11-11_1745_002.png [ 53.1 KiB | Viewed 3005 times ]
11 Nov 2017, 07:55
Kudos
Bookmarks
Bunuel
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
11 Nov 2017, 08:02
Kudos
Bookmarks
Bunuel
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)
