The budget for painting one side of the backdrop is $103222, and
the budget for the reflecting tape is $240.
It is given that the backdrop is in the hexagonal shape shown on the coordinate plane.
It is required to find the budget for painting one side of the backdrop and the budget for the reflecting tape.
What is a hexagon?
It is defined as a polygon that has 6 equal sides with an interior angle of 120° and an exterior angle is 60°.
We have a hexagon shown in the picture:
Since each unit on the coordinate plane represents 5 feet.
Hence each side length of the hexagon = 20 feet
The area of the hexagon:
[tex]\rm A = \frac{3\sqrt{3} }{2}a ^2[/tex] (a = 20 feet)
[tex]\rm A = \frac{3\sqrt{3} }{2}20 ^2[/tex]
A = 1.5×1.732×400
A = 1039.2 square feets
We are assuming the painting cost for each square unit is $10.
∴Total budget for painting one side of the backdrop = 1032.2×10
= $103222
We know the perimeter of the hexagon is given by:
P = 6a
P = 6×20
P = 120 feet
Again we are assuming that each unit cost for reflecting tape is $2.
∴Total budget for the reflecting tape:
= 120×2
= $240
Thus, the budget for painting one side of the backdrop is $103222, and
the budget for the reflecting tape is $240.
Learn more about the hexagon here:
https://brainly.com/question/3295271
