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 lb) l 0 0 l l 8 10lc) l 5 2 l l 3 8 ld) l 5 2 l l 8 10l
Accepted Solution
A:
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