To find the area of a triangle, we use the formula:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\][/tex]
In this problem, the height [tex]\( h \)[/tex] of the triangular floor is given as [tex]\( n \)[/tex] yards, and the base [tex]\( b \)[/tex] is given as 6 yards.
We can substitute these values into the area formula:
[tex]\[
\text{Area} = \frac{1}{2} \times (6 \, \text{yd}) \times (n \, \text{yd})
\][/tex]
First, multiply the base and height:
[tex]\[
6 \times n = 6n
\][/tex]
Then, multiply by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[
\text{Area} = \frac{1}{2} \times 6n = \frac{6n}{2} = 3n
\][/tex]
Thus, the expression that represents the area of the floor is:
[tex]\[
3n
\][/tex]
From the given options, the correct answer is:
[tex]\[ 3n \][/tex]
So, the expression representing the area of the attic floor is [tex]\( 3n \)[/tex].
