Sin(π/5)sin(x) + cos(x)cos(π/5) <= √2/2

Area of UN-SHADED region is 10x + 25

Step-by-step explanation:

Both figures are squares

The area of un-shaded region is the difference between the areas of the larger square and the smaller square

The formula of the area of a square is A = s², where s is the length of its side

∵ The length of the side of the larger square = (x + 5)

- Find its area using the formula above

∴ Area of the larger square = (x + 5)²

∵ The length of the side of the smaller square = x

- Find its area using the formula above

∴ Area of the smaller square = x²

∵ The area of un-shaded region = Area larger - Area smaller

∴ The area of un-shaded region = (x + 5)² - x²

- Simplify it

∵ (x + 5)² = (x)² + 2(x)(5) + (5)²

∴ (x + 5)² = x² + 10x + 25

- Substitute it in the expression above

∴ The area of un-shaded region = x² + 10x + 25 - x²

- Add like terms

∴ The area of un-shaded region = 10x + 25

- Put A represents the area of un-shaded region

∴ A = 10x + 25

Area of UN-SHADED region is 10x + 25