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20 Sep 2017, 22:57
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A
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Difficulty:
45%
(medium)
Question Stats:
68% (02:00) correct
32%
(01:54)
wrong
based on 106
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The figure above shows the lengths of the sides of an equiangular polygon. What is the area of the polygon?
(A) 7
(B) 8
(C) 9
(D) 14√2
(E) not determinable
Attachment:
2017-09-20_1022_001.png [ 6.6 KiB | Viewed 9707 times ]
20 Sep 2017, 23:55
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Given figure is Octagon => sum of angle = (8-2)*180
As all angles are equal : (8-2)*180/8 = 135
Find attached figure:
Octagon can be divided into 4 triangle and 5 rectangles.
While drawing rectangles we see angle of triangles formed is 45-45-90
Sides of triangles can be calculated = 1 => 1-1-\(\sqrt{2}\) triangle
So total area of given figure = 4 triangles + 5 rectangles formed = 4*(1/2 *1*1) + 5* (1*1) = 7
Answer: A
As all angles are equal : (8-2)*180/8 = 135
Find attached figure:
Octagon can be divided into 4 triangle and 5 rectangles.
While drawing rectangles we see angle of triangles formed is 45-45-90
Sides of triangles can be calculated = 1 => 1-1-\(\sqrt{2}\) triangle
So total area of given figure = 4 triangles + 5 rectangles formed = 4*(1/2 *1*1) + 5* (1*1) = 7
Answer: A
Attachments
Octagon.png [ 11.14 KiB | Viewed 8926 times ]
21 Sep 2017, 23:11
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Think of the entire figure as a square with corners cut out.
If you draw the corners back, you will see that they are 45-45-90 triangles with sqrt(2) as the hypotenuse. So each side of the triangle will be 1.
Area of figure = Area of square - Area of 4 triangles
Area of figure = 3^2 - 4*(1/2)*1*1 = 7
Answer(A)
If you draw the corners back, you will see that they are 45-45-90 triangles with sqrt(2) as the hypotenuse. So each side of the triangle will be 1.
Area of figure = Area of square - Area of 4 triangles
Area of figure = 3^2 - 4*(1/2)*1*1 = 7
Answer(A)
