Answer:
Part A)AT=16x^2
Part B)AT=4b^2 +12x^2
Step-by-step explanation:
Part A:
length of each side of square in tile=x
length of each small base side of trapezoid in tile=x
length of each large base side of trapezoid in tile=2x
height of each trapezoid in tile=x
Area of each square in tile= x^2
Area of each trapezoid in tile= x(x+2x)/2
= (3x^2)/2
area of squares inside tile= 4(x^2)
area of trapezoids inside tile= 8[(3x^2)/2]
Area of tile, AT= area of squares inside tile+area of trapezoids in tile
AT= 4(x^2) + 8[(3x^2)/2]
= 4x^2 + 12x^2
= 16x^2
Part B)
if If the tile is a square with a length of b centimeters then AT
= 4b^2 +12x^2 !
