A shipping comapny is designing new cardboard packages to sell to customers. The options are a rectangular prism, Box A, or a triangular prism, Box B. Which box is made with less cardboard?
+934 An area of a prism is the area of the base time the height. Box A's area is just 4 * 10 * 3= 120in^3. Box B's area is the area of the base triangle (8/2) * 3= 12 times the height 6, so 12 * 6= 72in^3. Since 120>72, Box B is made of less cardboard.
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this has nothing to do with volume.
BOX A
2 side of 3"x4" = Side A
2 side 10"x3"= Side B
2 side 10"x4" = Side C
therefore
area of Side A + Area of Side B + Area of Side C = total carboard
so
2(3x4) + 2(10x3) + 2(10x4)
2(12) + 2(30) + 2(40)
24 + 60 + 80
TOTAL AREA BOX A = 164 square inches
BOX B
Area of a right triangle is 1/2 x base x height (can also be expressed as "0.5 x base x height" or "(base x height)/2" )
therefore
both triangular sides have 2 right trianges each.
this means we have
2 sides (0.5 x 8 x 3) x 2 which reduces to: 2 sides of 8 x 3 (beause the .5 and the 2 cancel each other out)
therefore we have in total
2 sides of 8 x 3
1 side of 8 x 6
2 sides 5 x 6
therefore
2(8 x 3) + (8 x 6) + 2(5 x 6)
2(24) + (48) + 2(30)
48 + 48 + 60
TOTAL AREA BOX B = 156 square inches
