Answer:
The area of the triangular garden is [tex]173\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The equilateral triangle has three equal sides and three equal internal angles (the measure of each internal angle is 60 degrees)
The area of a triangle applying the law of sines is equal to
[tex]A=\frac{1}{2}(a)(b)sin(C)[/tex]
In this problem we have a equilateral triangle
therefore
[tex]a=b=20\ ft[/tex]
[tex]C=60\°[/tex]
substitute
[tex]A=\frac{1}{2}(20)(20)sin(60\°)[/tex]
[tex]A=\frac{1}{2}(20)(20)\frac{\sqrt{3}}{2} \\ \\A=100\sqrt{3}\ ft^{2}\\ \\A=173\ ft^{2}[/tex]
