To find how much larger the area of the new pen is compared to the current pen, we start by calculating the area of both the current and new pens.
-
Current area of the pen: The current pen is square with each side measuring 10 feet. The area \( A \) of a square is calculated as: \[ A = \text{side}^2 \] So, the area of the current pen is: \[ A_{\text{current}} = 10^2 = 100 \text{ ft}^2 \]
-
New side length of the pen: The farmer plans to increase each side to 160% of its current measure. We calculate 160% of 10 feet: \[ \text{New side length} = 10 \times 1.60 = 16 \text{ feet} \]
-
New area of the pen: Now we can find the area of the new pen using the new side length: \[ A_{\text{new}} = 16^2 = 256 \text{ ft}^2 \]
-
Increase in area: The increase in area is then calculated by subtracting the current area from the new area: \[ \text{Increase in area} = A_{\text{new}} - A_{\text{current}} = 256 \text{ ft}^2 - 100 \text{ ft}^2 = 156 \text{ ft}^2 \]
The area of the new pen is 156 ft² larger than the area of the current pen.
So, the answer is: 156 ft².
1 answer