Which will give the area of a parallelogram with the vertices (0, 0), (5, 2), (8, 10), and (3, 8)? a) l 0 0 l    l 3 8 l b) l 0 0 l    l 8 10l c) l 5 2 l    l 3 8 l d) l 5 2 l    l 8 10l

Sketch the parallelogram as shown below.

The area of ΔABD is one-half of the area of the parallelogram because of symmetry.
Calculate lengths a,b,c of the triangle.
a = √(5² + 2²) = √29.
b = √(2² + 6²) = √40
c = √(3² + 8²) = √73
Calculate the area of ΔABD (by Horner's Rule).
s = (1/2)*(a + b + c) = 10.1269
s - a = 4.7417
s - b = 3.8023
s - c = 1.5829
Area = √[s(s-a)(s-b)(s-c)] = √(289) = 17
The area of the parallelogram is 2*17 = 34.

Evaluate the given determinants. The correct answer should be 34.
a) 0*8 -0*3 = 0
    Incorrect

b) 0*10 - 0*8 = 0
    Incorrect

c) 5*8 - 2*3 = 34
    Correct

d) 5*10 - 2*8 = 34
    Correct

  (c) or (d) will give the correct area.

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