On the xy plane, what is the unit area of the quadrilateral defined by

Question

On the xy plane, what is the unit area of the quadrilateral defined by the xy coordinate pairs (-1,-1), (-5,3), (2,-1), and (2,3)?

(A)  12\sqrt{2}

(B)  11\sqrt{3}

(C) 18

(D) 20

(E) 25

yashikaaggarwal · Answer

Area Of Triangle ABC with coordinates (-1,-1), (-5,3), (-1,3)
A = (1/2)  
A = (1/2)  
A = (1/2)  
A = (1/2)  
A = 1/2*16
A = 8

Area Of Rectangle BCDE = BC*CD
Length of BE^2 = (y2-y1)^2+(x2-x1)^2
Length of BE^2 = (3+1)^2+(-1+1)^2
Length of BE^2 = (4)^2+(0)^2
Length of BE = 4

Length of BC^2 = (y2-y1)^2+(x2-x1)^2
Length of BC^2 = (3-3)^2+(2+1)^2
Length of BC^2 = (0)^2+(3)^2
Length of BC = 3

AREA = 4*3 = 12

Total area = 12 + 8 = 20

Answer is D

dep · Answer

Posted from my mobile device

CrackverbalGMAT · Answer

Referring to the diagram below, let A = (-1,-1), B = (2,-1), C = (2,3) and D = (-5,3)

The diagram is a Trapezium of height = 4 units (3 units above the x axis and 1 unit below)

Area of the Trapezium =  \frac{h}{2}*

Length AB = 3 (2 units to the right of y axis and 1 unit to the left)

Length CD = 7 (2 units to the right of y axis and 5 units to the left)

The area =  \frac{4}{2}*    = 2 * 10 = 20

Option D

Arun Kumar

Prep Toolkit