Paulina is remodeling her bathroom. The tile she has chosen is shown below. There are squares and trapezoids in the tile. The side length of each square in the tile is x centimeters. The height and the length of one of the bases of each trapezoid is x centimeters. The other length is 2x centimeters.

a tile with four small squares at the center and eight trapezoids around the border (two on each side), all in alternating colors

Part A
Write a simplified equation to solve for x in terms of AT, the area of the tile. If necessary, use rational coefficients instead of root symbols.

Question

Paulina is remodeling her bathroom. The tile she has chosen is shown below. There are squares and trapezoids in the tile. The side length of each square in the tile is x centimeters. The height and the length of one of the bases of each trapezoid is x centimeters. The other length is 2x centimeters.

a tile with four small squares at the center and eight trapezoids around the border (two on each side), all in alternating colors

Part A
Write a simplified equation to solve for x in terms of AT, the area of the tile. If necessary, use rational coefficients instead of root symbols.

aleks · Answer

80 because

4x4=16 and 16x2= 32, and 4x8= 32 and 32x2=64, and

64+32=80