**Solution:**

The given equation of the parabola is y² = 8x. Let's find the coordinates of the point on the parabola where the tangent and normal are drawn.

**Finding the Coordinates of the Point on the Parabola:**

We are given that the tangent and normal are drawn at the point (8,8) on the parabola. To find the coordinates of the point on the parabola, we substitute x = 8 into the equation y² = 8x.

y² = 8 * 8
y² = 64
y = ±√64
y = ±8

So, the coordinates of the point on the parabola where the tangent and normal are drawn are (8, 8) and (8, -8).

**Finding the Slope of the Tangent:**

To find the slope of the tangent at the point (8, 8), we differentiate the equation of the parabola implicitly with respect to x.

Differentiating both sides of y² = 8x with respect to x:
2yy' = 8

Substituting the x-coordinate of the point (8, 8) into the equation, we get:
2(8)y' = 8
16y' = 8
y' = 8/16
y' = 1/2

So, the slope of the tangent at the point (8, 8) is 1/2.

**Finding the Slope of the Normal:**

The slope of the normal to a curve at a given point is the negative reciprocal of the slope of the tangent at that point. Therefore, the slope of the normal at the point (8, 8) is -2.

**Finding the Equation of the Tangent:**

To find the equation of the tangent at the point (8, 8), we use the point-slope form of a line:

y - y₁ = m(x - x₁)

Substituting the values into the equation, we get:
y - 8 = (1/2)(x - 8)
2y - 16 = x - 8
x - 2y = -8

So, the equation of the tangent at the point (8, 8) is x - 2y = -8.

**Finding the Equation of the Normal:**

Similarly, to find the equation of the normal at the point (8, 8), we use the point-slope form of a line:

y - y₁ = m(x - x₁)

Substituting the values into the equation, we get:
y - 8 = -2(x - 8)
y - 8 = -2x + 16
2x + y = 24

So, the equation of the normal at the point (8, 8) is 2x + y = 24.

**Finding the Area of the Triangle:**

To find the area of the triangle formed by the tangent and normal at the point (8, 8), we need to find the coordinates of the intersection point of the tangent and normal.

Solving the equations of the tangent and normal, we get:
x - 2y = -8
2x + y = 24

Multiplying the second equation by 2, we get:
4x + 2y