Area Under Simple Curves

Consider the region R = {(x,y) ∈ R²: x² ≤ y ≤ 2x}. If a line y=α divides the area of region R into two equal parts, then which of the following is true?

Let a,b,c,d and p be any non-zero distinct real numbers such that (a²+b²+c²)p² - 2(ab+bc+cd)p + (b²+c²+d²)=0. Then:

The area (in sq. units) of the region, given by the set {(x,y) ∈ R*R | x ≥ 0, 2x² ≤ y ≤ 4 – 2x} is:

If the area of the bounded region R = {(x,y) : max{0, logₑx} ≤ y ≤ 2ˣ, 1/2 ≤ x ≤ 2} is, α(logₑ2)⁻¹ + β(logₑ2) + γ, then the value of (α + β - 2γ)² is equal to: