Determine the most precise name for the quadrilateral. Then find its area. P(0,3) Q(4,3) R(-2,-3) S(-6,-3)

Question

A. The quadrilateral PQRS is a square.

B. The quadrilateral PQRS is a parallelogram.

C. The quadrilateral PQRS is a trapezoid.

D. The quadrilateral PQRS is a isoseceles trapezoid.

E. The quadrilateral PQRS is a rhombus.

F. The quadrilateral PQRS is a rectangle.

G. The quadrilateral PQRS is a kite.

 

Calculate the area of PQRS. 

Answer 1

If you plot the 4 points you have a parallelogram

 

the bottom side is from (-6,-3) to (-2,-3)

The top is from (0,3) to (4,3)

This gives a base length of 4 since the distance

from (-6,-3) to (-2,-3) = 4

as does the distance from (0,3) to (4,3)

 

The sides are the connecting lines from (0,3) to (-6,-3)

and from (4,3) to (-2,-3).  The vertical height is -3 up to 3 or 6

 

The area of the parallelogram is base*height = 4(6) = 24