Given, equation of circle is 

      x² + y² = 16

=> x² + y² = 4²

=> y² = 4² - x² 

=> Y = √(4² - x² )

Now, area of the circle is defined as A = ₀∫⁴ √(4² - x² ) dx 

=> A = (1/2) * [x√(4² - x² ) + 4² * sin^-1 (x/4) ₀]⁴            {apply √(a² - x² ) formula}

=> A = (1/2) * [16 * sin^-1 (4/4)]

=> A = 8 * sin^-1 (1)

=> A = 8 * π/2

=> A = 4π 

So, the area of the circle x² + y² = 16 is 4π