Answer:
They gained 4 1/2 yards
Step-by-step explanation:
It was a positive gain because they didn't go back.
Area of the trapezoid:

Area of the rectangle:
4.2 x 3.1 = 13.02 cm^2
Area of each quarter circle:

We have two quarter circles:
7.54 + 7.54 = 15.08
41.65 + 13.02 + 15.08 = 69.75 cm^2
Sizes? Of the wall and paper?
Answer:
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Step-by-step explanation:
Arc length of a parametric curve is:
L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
x = t + cos t, dx/dt = 1 − sin t
y = t − sin t, dy/dt = 1 − cos t
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Or, if you wish to simplify:
L = ∫₀²ᵖⁱ √(1 − 2 sin t + sin²t + 1 − 2 cos t + cos²t) dt
L = ∫₀²ᵖⁱ √(3 − 2 sin t − 2 cos t) dt