Question

Prudence is creating a garden in her backyard. She wants it to be the shape of an equilateral triangle with sides of length 20 feet. What will be the area of this triangular garden? Round your answer to the nearest whole foot.

Answer 1

Answer:

The area of the triangular garden is $173\ ft^{2}$  

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

$A=\frac{1}{2}(a)(b)sin(C)$

In this problem we have a equilateral triangle

therefore

$a=b=20\ ft$

$C=60\°$

substitute

$A=\frac{1}{2}(20)(20)sin(60\°)$

$A=\frac{1}{2}(20)(20)\frac{\sqrt{3}}{2} \\ \\A=100\sqrt{3}\ ft^{2}\\ \\A=173\ ft^{2}$