All of the sides in the figure above are the same length. in addition, sides x and z are parallel and sides w and y are parallel. what is the most specific term for this figure? square rhombus trapezoid quadrilateral rectangle

The first thing we have is the following statements:
 "All of the sides in the figure are the same length":
 x = z = w = y
 "In addition, sides x and z are parallel and sides w and y are parallel":
 x ll z and w ll y
 Both statements define a square.
 
 The most specific term for this figure is:
 Square

the height of the lamppost is 2.7 meters.

Step-by-step explanation:

Proportion states that two ratios or fractions are equal.

As per the statement:

A boy who is 1.8 meters tall stands 1 meter away from a lamppost and casts a shadow 2 meters long.

You can see the diagram as shown below.

by definition of proportion we have;

From the diagram:

height of the boy = 1.8 meter tall , shadow of the boy = 2 meter long, height of the lamppost = h meter and shadow of the lamppost = 1+2 = 3 meter

⇒

Multiply both sides by 3 we have;

2.7 = h

or

h = 2.7 meter

Therefore, the height of the lamppost is 2.7 meters.