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

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