There are 4 identical wooden blocks that are 20 inches long, 2 inches wide and 1 inch thick. If you glue them together, what is the difference
of the largest and smallest outer surface area you can get?

Step-by-step explanation:

Each block has two 20×1 faces, two 20×2 faces, and two 2×1 faces.

Surface area of one block = 2(20×1) + 2(20×2) + 2(2×1) = 124 sq in

Total surface area = 4(124) = 496 sq in.

Largest surface area: Assemble the blocks end-to-end into a block that is 80 by 2 by 1. Six of the 2 by 1 faces are hidden, so the surface area is 496 - 6(2×1) = 484 sq in.

Smallest surface area: Assemble the blocks into a block that is 20 by 4 by 2. Four of the 20 by 2 faces and four of the 20 by 1 faces are hidden, so the surface area is 496 - 4(20×2) - 4(20×1) = 256 sq in.

Difference in surface area = 484-256 = 228 sq in.

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the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .