A property had been a rectangular 100-by-200-ft parcel. The new zoning map
changed the boundaries so that the property is now shaped like a parallelogram.
The landowner complained that this represents a loss of area. Do you agree? If
so, what is the loss in square feet?

Yes there is a loss of area

The loss is 5,858 ft²

Step-by-step explanation:

Kindly find attached rough sketch of the problem for your reference.

This problem bothers on the mensuration of flat shapes, rectangle and parallelogram

Firstly let us calculate initial area of the map, the rectangle

Area = length x width

Area = 200*100

Area = 20,000ft²

Now let us calculate the area of the new zoning map, parallelogram

Area = Base x height

But from the sketch we can solve for the height Applying

SOH CAH TOA

Using SOH

Sinθ= opposite/hypotenuse

Sin θ= h/100

h= sinθ*100

h= sin(45)*100

h= 0.7071*100

h= 70.71ft

We can now solve for the area of the new zoning map

A= 200*70.71

A= 14142ft²

Loss in square feet is

Area of initial map - area of New map

= 20,000-14,142

= 5,858 ft²

wheres graph

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.