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## What is the area of the parallelogram ABCD? A = (1, 1), B = (2, 2), C = (5, 2), and D = (4, 1) (GMAT-MATHS)

##### What is the area of the parallelogram ABCD? A = (1, 1), B = (2, 2), C = (5, 2), and D = (4, 1)a. 3b. 4c. 41/2d. 9e. 10

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Area of parallelogram    = 2 × Area of ∆ABC

= 2 × 1/2 × base × height sq. units

= 2 × 1/2 × AB × CE sq. units

= b × h sq. units

= base × height sq. units

The area is then given by the formula
area
=
(
x
1
y
2
y
1
x
2
)
+
(
x
2
y
3
y
2
x
3
)
.....
+
(
x
n
y
1
y
n
x
1
)
2

Where x1 is the x coordinate of vertex 1 and yn is the y coordinate of the nth vertex etc. Notice that the in the last term, the expression wraps around back to the first vertex again.

Area is 3

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