Equilateral Triangles
An equilateral triangle has all of its three sides of the same measure. Suppose the side length of an equilateral triangle is L.
The perimeter of such a triangle is:
P = 3L
Phyllis bought 21 feet of wood to frame a triangular window. This corresponds to the perimeter of the triangle, so we can calculate the side length:
L = P/3
L = 21 feet / 3
L = 7 feet.
Now we know the length of the side of the triangle, we calculate the area by using the formula:
[tex]A=\frac{\sqrt[]{3}}{4}L^2[/tex]
Substituting L = 7 feet:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(7ft)^2 \\ A=\frac{\sqrt[]{3}}{4}49ft^2 \\ \text{Calculating:} \\ A\approx21.22ft^2 \end{gathered}[/tex]
