Answer:
47.4 pounds
Step-by-step explanation:
First, find the height of the trapezoid. Draw the height DE. Quadrilateral ABED is a rectangle, then BE = 12 cm. Since BC = 20 cm, then EC = 20 - 12 = 8 cm.
Consider right triangle DEC. By the Pythagorean theorem,
[tex]DE^2+EC^2=CD^2\\ \\DE^2+8^2=17^2\\ \\DE^2=289-64\\ \\DE^2=225\\ \\DE=15\ cm[/tex]
The area of the trapezoid ABCD is
[tex]A=\dfrac{AD+BC}{2}\cdot DE=\dfrac{12+20}{2}\cdot 15=16\cdot 15=240\ cm^2[/tex]
One can cover [tex]100\ cm^2[/tex], then it is needed
[tex]\dfrac{240}{100}=2.4[/tex] cans
One can costs 19.75 pounds, then 2.4 cans cost
[tex]19.75\cdot 2.4=47.4[/tex] pounds
