Answer:
The area of the rectangle is approximately 885.3333333333333 ft² (rounded to two decimal places).
Step-by-step explanation:
We can find the area of the rectangle by following these steps:
Simplify the width:
The width is given as 3 √64^2 ft.
We know 64^2 is equal to 64 x 64 = 4096.
Therefore, the width is 3√4096 ft.
Convert the mixed number length to a fraction:
The length is given as 27 2/3 ft.
Represent the whole number part of the mixed number as a fraction with the same denominator (3) as the fractional part: 27 * (3/3) = 81/3 ft
Now you have the whole number part and the fractional part in terms of thirds: 81/3 + 2/3
Combine the two fractions to get a single fraction representing the total length: (81 + 2)/3 ft = 83/3 ft
Calculate the area:
Area of a rectangle = width x length
Area = 3√4096 ft * 83/3 ft
Simplify the expression (optional):
We can simplify the expression further, but it's not necessary for most calculators.
Finding the area using a calculator:
Most calculators can handle mixed numbers and square roots directly. You can simply input the expression:
3 * sqrt(4096) * (83/3)
