Find the perimeter and area of each figure.

  1. A = 2x; P = 4x+2. A = 4; P = 10.

  2. A = y² +2; P = 4y +2. A = 27; P = 22.

Step-by-step explanation:

1. The area is the sum of the marked areas of each of the tiles:

  A = x + x

  A = 2x

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The perimeter is the sum of the outside edge dimensions of the tiles. Working clockwise from the upper left corner, the sum of exposed edge lengths is ...

  P = 1 + (x-1) + x + 1 + (x+1) + x

  P = 4x +2

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When x=2, these values become ...

  A = 2·2 = 4 . . . . square units

  P = 4·2+2 = 10 . . . . units

2. Again, the area is the sum of the marked areas:

  A = y² + 1 + 1

  A = y² +2

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The edge dimension of the square y² tile is presumed to be y, so the perimeter (starting from upper left) is ...

  P = y +(y-2) +1 +2 +(y+1) +y

  P = 4y +2

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When y=5, these values become ...

  A = 5² +2 = 27 . . . . square units

  P = 4·5 +2 = 22 . . . . units

expression #3 is not equivalent. the others are.