What is the area of this rectangle?
The length is given by the expression (5/4)b + 20 ft and the width is (4/5)b ft.
The area of the rectangle is ________________
(Use the operation symbols in the math palette as needed. Simplify your answer.)
What is the area of this rectangle?
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To find the area of a rectangle, you use the formula:
[
text{Area} = text{Length} times text{Width}
]
Here, the length is given as ((frac{5}{4})b + 20) ft and the width as ((frac{4}{5})b) ft.
Now, let’s calculate the area:
[
text{Area} = left(frac{5}{4}b + 20right) times left(frac{4}{5}bright)
]
To simplify this, we can distribute:
1. Multiply (frac{4}{5}b) by each term in the parentheses.
2. The first term will be:
[
frac{5}{4}b times frac{4}{5}b = b^2
]
3. The second term will be:
[
20 times frac{4}{5}b = 16b
]
Now combining these, we get:
[
text{Area} = b^2 + 16b
]
So, the area of the rectangle is:
[
boxed{b^2 + 16b} text{ ft}^2
]
This expression represents the area in terms of (b). If you need further assistance with this, feel free to check out our