Question

the function a described by ( a(s) = \frac{sqrt{3}}{4} s^2 ) gives the area of an equilateral triangle with side ( s ). find the area when a side measures 14 cm. the area is (square) (simplify your answer. type an exact answer, using radicals as needed)

Explanation:

Step1: Substitute \( s = 14 \) into the formula \( A(s)=\frac{\sqrt{3}}{4}s^{2} \)

\( A(14)=\frac{\sqrt{3}}{4}\times(14)^{2} \)

Step2: Calculate \( (14)^{2} = 196 \)

\( A(14)=\frac{\sqrt{3}}{4}\times196 \)

Step3: Simplify \( \frac{196}{4}=49 \)

\( A(14) = 49\sqrt{3} \)

Answer:

\( 49\sqrt{3} \)