Answer:
in steps
Step-by-step explanation:
upper square: P = 20x² + 8
side: P/4 = 5x² + 2
A = side² = (5x² + 2)² = 25x⁴ + 20x² + 4
Middle equilateral Triangle: A = x² + 4x + 4 base = 2x + 4
A = base x height / 2
(x + 2)² = 2 (x + 2) x height /2
height = x + 2
perimeter = 2 (x + 2) x 3 = 6x + 12
Lower trapezoid: A₁ = 2x² + 24x + 40 = 2 (x² + 12x + 20) = 2 (x + 2) (x + 10)
A₁ = (x + 10)² = 2 (x + 2) (x + 10)
x + 10 = 2x + 4
x = 6
A₂ = (2x + 4) (x + 10) / 2 = (16 x 16) / 2 = 128
A₁ = (6 + 10)² = 256
AT = 256 + 128 = 384
