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.

The answer would be a

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.