Answer:
Part A) see the explanation
Part B) 56 square centimeters
Part C) One piece of sandpaper is not enough to sand all the edges on both sides
Step-by-step explanation:
The picture of the question in the attached figure
Part A) List all the dimensions of one trapezoid face. What are the lengths of the 2 bases of the trapezoid? What is the height of each trapezoid face?
we know that
In a trapezoid we have
b_1 and b_2 are the parallel sides of trapezoid
h is the height of trapezoid (perpendicular distance between the parallel sides)
we have
The lengths of trapezoids are
[tex]b_1=8\ cm\\b_2=6\ cm[/tex]
The height of trapezoid is
[tex]h=4\ cm[/tex]
The inclined side of trapezoid is
[tex]c=4.47\ cm[/tex]
Part B) Use the information from part a to answer, Surfaces A and B will be painted blue. What is the total area that will be painted blue?
we know that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}[b_1+b_2]h[/tex]
we have
[tex]b_1=8\ cm\\b_2=6\ cm[/tex]
[tex]h=4\ cm[/tex]
substitute in the formula
[tex]A=\frac{1}{2}[8+6](4)=28\ cm^2[/tex]
Multiply the area by 2 (Surface A and Surface B)
so
[tex]28(2)=56\ cm^2[/tex]
Part C) The faces A and B need to be sanded. A piece of sandpaper advertises that it can sand up to 20 cm. Will one piece of sandpaper be enough to sand all the edges of both faces?
we know that
The perimeter of a trapezoid is equal to the sum of its four sides
[tex]P=8+4+6+4.47=22.47\ cm[/tex]
The perimeter of two trapezoids is equal to
[tex]22.47(2)=44.94\ cm[/tex]
[tex]44.94\ cm > 20\ cm[/tex]
therefore
One piece of sandpaper is not enough to sand all the edges on both sides
