Bunuel

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
Attachment:
The attachment 2017-10-31_1105.png is no longer available
Attachment:
areasq.png [ 10.22 KiB | Viewed 4581 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) =
4Right side of extended figure = CD + EF =
4All 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