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In the figure, angles A, B, C, D, E, F, G, H are all 90° and AB = AH =

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Joined: 02 Sep 2009
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Kudos [?]: 135946 [0], given: 12716

In the figure, angles A, B, C, D, E, F, G, H are all 90° and AB = AH = [#permalink]

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New post 30 Oct 2017, 23:06
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

81% (02:41) correct 19% (01:37) wrong based on 26 sessions

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In the figure, angles A, B, C, D, E, F, G, H are all 90° and AB = AH = EF = DE. Also, BC = CD = HG and the Cartesian coordinates of A, C, and E are (1, 2), (2, 5), and (5, 4), respectively. What is the area of figure ABCDEFG?

(A) 6
(B) 7
(C) 8
(D) 10
(E) 12

[Reveal] Spoiler:
Attachment:
2017-10-31_1105.png
2017-10-31_1105.png [ 6.61 KiB | Viewed 638 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135946 [0], given: 12716

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Joined: 05 Dec 2016
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Kudos [?]: 27 [0], given: 49

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Re: In the figure, angles A, B, C, D, E, F, G, H are all 90° and AB = AH = [#permalink]

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New post 31 Oct 2017, 05:30
Basing on the information goven, we can find as follows:
B (1,5)
D (2,4)
G (4,0)
F (5,0)
H (5,1)

Figure consists of 1 main rectangle with 2 side squares.
Using values found above we can calculate corresponding areas.

main rectangle=2*4
side square=1*1=1
area of main figure= 8+1*2=10
Answer D

Kudos [?]: 27 [0], given: 49

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Kudos [?]: 407 [0], given: 647

Re: In the figure, angles A, B, C, D, E, F, G, H are all 90° and AB = AH = [#permalink]

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New post 31 Oct 2017, 11:18
Bunuel wrote:
Image
In the figure, angles A, B, C, D, E, F, G, H are all 90° and AB = AH = EF = DE. Also, BC = CD = HG and the Cartesian coordinates of A, C, and E are (1, 2), (2, 5), and (5, 4), respectively. What is the area of figure ABCDEFG?

(A) 6
(B) 7
(C) 8
(D) 10
(E) 12

[Reveal] Spoiler:
Attachment:
The attachment 2017-10-31_1105.png is no longer available

Attachment:
areasq.png
areasq.png [ 10.22 KiB | Viewed 350 times ]

Find the side lengths of what would be a square.

(Area of square) - (area of cut-out pieces) = area of figure

1) Find length of BC

B's coordinates? All angles are 90°, so

B has the same x-coordinate as A and the same y-coordinate as C

B (1,5)

Length of BC? Difference between x-coordinates of B and C

(2 - 1) = 1 = BC length (=CD and HG)

2) Find length of AB = difference of y-coordinates for A and B

(5 - 2) = 3 = AB length = AH, EF, and DE

3) Find F's coordinates

Same x-coordinate as E: 5

y coordinate of F?
(y-coordinate of E) - (length of EF) = y-coordinate of F
F's y-coordinate: 4 - 3 = 1

F's coordinates: (5,1)

4) Known values:
Top side of extended figure = (BC + DE) = 4

Right side of extended figure = CD + EF = 4

All angles are 90° - this is a square

5) We need GF length

Bottom gray line is parallel to AH

Length of bottom side TOTAL is (F's x-coordinate) - (A's x-coordinate) = (5 - 1) = 4

GF length? Total length - AH
(4 - 3) = 1 = GF length

6) Area of ABCDEFGH?

(Area of would-be square) - (area of two cut-out pieces)
(4 * 4) - 2(3 * 1) = (16 - 6) = 10

Answer D

Kudos [?]: 407 [0], given: 647

Re: In the figure, angles A, B, C, D, E, F, G, H are all 90° and AB = AH =   [#permalink] 31 Oct 2017, 11:18
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In the figure, angles A, B, C, D, E, F, G, H are all 90° and AB = AH =

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