of area from the prism is also not exposed. Total area concealed =
16 sq. ft + 16 sq. ft. = 32 sq. ft. Now find the total surface area of
the table’s individual parts.
SA of one cube = 6(2 feet)^2 = 6(4 sq. ft.) = 24 sq. ft.
SA of four congruent cubes = 4 ×24 sq. ft. = 96 sq. ft.
SA of one rectangular prism = 2(15 ft.(7 ft.) + 7 ft.(1 foot) + 15
ft.(1 foot)) = 2(105 sq. ft. + 7 sq. ft. + 15 sq. ft.) = 2(127 sq. ft.) =
254 sq. ft.
Total SA = 96 sq. ft. + 254 sq. ft. = 350 sq. ft.
Finally, subtract the concealed surface area from the total
surface area = 350 sq. ft. – 32 sq. ft = 318 sq. ft.
- 4 bottles.Since this is a triangular prism, break it into it individual
parts. First calculate the area of the triangular face, or door of the
tent. A= ^12 (b)(h) = ^12 (8)(5) = 20 ft^2. Since there are triangular doors
at the front and the back, double this to get 40 ft^2. Next, the
bottom of the tent will be a rectangle that is 8 feet by 14 feet, so A
= (w)(l) = (8)(14) = 112 ft^2. The two remaining sides are a little
trickier because the Pythagorean theorem will be needed to solve
for the “width” or hypotenuse of the front triangular face: a^2 + b^2 =
c^2 , 4^2 + 5^2 = 16 + 25 = 41 = c^2 , so c= 6.4 feet. Use this as the width
of the two slanting sides of the tent that have a length of 14. A=
(w)(l) = (6.4)(14) = 89.6 ft2. Since there are two of these sides,
double 89.6ft^2 to get 179.2 ft^2 as the surface area for the two
slanted sides of the tent. Add all of the subtotals together to get:
40ft^2 + 112ft^2 + 179.2 ft^2 = 331.2 ft^2. Since each bottle of
waterproof coating will just cover 100 square feet, Victoria will
need to buy 4 bottles.
- Surface Area= 297.5 sq. in.The three blocks are congruent; find
the surface area of one block and multiply it by three: SA = 2(8.3
in.(4.0 in.) + 4.0 in.(1.7 in.) + 8.3 in.(1.7 in.) = 2(33.2 sq. in. + 6.8
sq. in. + 14.11 sq. in.) = 2(54.11 sq. in.) = 108.22 sq. in. 108.22 sq.
in. ×3 = 324.66 sq. in. Look at the diagram: The ends of the
middle block are concealed, and they conceal an equal amount of
space on the other two blocks where they are joined: 2 ×2(4.0 in.
(1.7 in.) = 27.2 sq. in. Subtract the concealed surface area from
the total surface area: 324.66 sq. in. – 27.2 sq. in. = 297.46 sq. in.
501 Geometry Questions
