What is the area of parallelogram abcd?
11 square units
13 square units
15 square units
16 square units

Option B. 13 square units

Step-by-step explanation:

Area of a parallelogram is defined by the expression

A = × (Disatance between them)

Vertices of A, B, C and D are (3, 6), (6, 5), (5, 1) and (2, 2) respectively.

Length of AB =

                      =

                      =

Since length of opposite sides of a parallelogram are equal therefore, length of CD will be same as

Now we have to find the length of perpendicular drawn on side AB from point D or distance between parallel sides AB and CD.

Expression for the length of the perpendicular will be =

Slope of line AB (m) =

                                 =

Now equation of AB will be,

y - y' = m(x - x')

y - 6 =

3y - 18 = -(x - 3)

3y + x - 18 - 3 = 0

x + 3y - 21 = 0

Length of a perpendicular from D to side AB will be

=

=

Area of parallelogram ABCD =

=

=

= 13 square units

Option B. 13 units will be the answer.

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: