To find the area of the opening of the doorway that Enrique is constructing, we need to first calculate the dimensions of the doorway.
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Width of the Doorway:
The width of the doorway is given as \(2\sqrt{3}\) feet which was cut from an 8-foot board. Therefore, the width \(W\) of the doorway is: \[ W = 2\sqrt{3} \text{ feet} \] -
Height of the Doorway:
The length \(2\sqrt{3}\) feet that was cut from the first 8-foot board is then attached to another 8-foot board, which we use to frame the height of the door. The height \(H\) of the doorway is therefore: \[ H = 2\sqrt{3} \text{ feet} \] -
Area of the Opening:
The area \(A\) of the opening of the doorway can be calculated using the formula for the area of a rectangle: \[ A = \text{Width} \times \text{Height} \]Substituting in our values for \(W\) and \(H\): \[ A = (2\sqrt{3}) \times (2\sqrt{3}) \] \[ A = 4 \times 3 \] \[ A = 12 \text{ square feet} \]
Thus, the area of the opening of the doorway Enrique is building is \(\boxed{12}\) square feet.
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