Sure, let's solve the problem step by step.
You are given the base [tex]\( (b) \)[/tex] and height [tex]\( (h) \)[/tex] of a triangle and need to find the area using the formula for the area of a triangle:
[tex]\[ \text{Area} = \frac{1}{2} \times b \times h \][/tex]
Given values:
[tex]\[ b = 18 \][/tex]
[tex]\[ h = 2 \sqrt{3} \][/tex]
First, let's substitute [tex]\( h = 2 \sqrt{3} \)[/tex]:
[tex]\[ h = 2 \sqrt{3} \approx 3.4641 \][/tex]
Now, substitute the given values of [tex]\( b \)[/tex] and [tex]\( h \)[/tex] into the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times 18 \times 3.4641 \][/tex]
Next, multiply [tex]\( 18 \)[/tex] by [tex]\( 3.4641 \)[/tex]:
[tex]\[ 18 \times 3.4641 = 62.9286 \][/tex]
Then, multiply this result by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ \frac{1}{2} \times 62.9286 = 31.1769 \][/tex]
Thus, the area of the triangle is approximately:
[tex]\[ \text{Area} \approx 31.1769 \][/tex]
So the values for [tex]\( b \)[/tex] (base), [tex]\( h \)[/tex] (height), and the area of the triangle are:
[tex]\[ b = 18 \][/tex]
[tex]\[ h \approx 3.4641 \][/tex]
[tex]\[ \text{Area} \approx 31.1769 \][/tex]
