Answer:
3) 522
4) 468
Step-by-step explanation:
hello!
3) in the question, it says the cross section is a square, and the area of PQRS is 81.
for the square, we know that the length and height have to be the same, so if the area is 81, then we know the sides are both 9 because 9*9 is 81 and they're the same numbers multiplied. (same height and length)
with the information that all 4 sides of the square is 9 and the other side is labeled 10, we can figure out the rest.
both squares : 81+81=162
both 10 by 9 sides: 90+90=180
both 10 by 9 sides (top and bottom): 90+90=180
total surface area=162+180+180=522
4) for this problem, we can see that the triangle is a right triangle.
to solve the area of the triangle, we can do (9*12)/2=108/2=54.
there are two sides with triangles, so we double 54 (54*2=108)
9 by 10 side: 90
10 by 12 side: 120
now for the last slide, theres no information on the length. the formula for the diagonal is
a^2+b^2=c^2
which is
9^2+12^2=81+144=255=15^2
with this, the area of the rectangular side gives us 10*15 which is 150.
adding it together, we get
108+90+120+150=468.
hope this helps!
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