Final answer:
To find the approximate area of the top of the table, use the Pythagorean theorem to determine the length of the table and then multiply it by the width.
Step-by-step explanation:
To find the approximate area of the top of the rectangular table, we need to use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side, which is the hypotenuse.
In this case, the width of the table is one of the shorter sides, and the diagonal is the hypotenuse. Let's denote the length of the table as L. Using the Pythagorean theorem, we can write the equation as:
L² + 56² = 64²
Simplifying the equation, we get:
L² = 64² - 56²
L² = 4096 - 3136
L² = 960
Taking the square root of both sides, we get:
L = √960
L is approximately 31 inches. The length of the table is 31 inches.
The approximate area of the top of the table can be found by multiplying the length and the width:
Area = 31 inches x 56 inches
Area = 1736 square inches