Final answer:
The approximate height of the section Lane paints is approximately 6.782 inches.
Step-by-step explanation:
The area of a square is found by squaring the length of one side. In this case, we have a square-shaped section of a fence with an area of 46 square inches. To find the approximate height of the section, we need to find the length of one side. Let's call the length of one side 'x' inches.
Using the formula for the area of a square, we have x^2 = 46. To solve for x, we can take the square root of both sides: sqrt(x^2) = sqrt(46). Therefore, x ~ 6.782.
Since the section is square-shaped, the height is equal to the length of one side. Therefore, the approximate height of the section Lane paints is approximately 6.782 inches.