A.) Given the altitude of the equilateral triangle, find the side.
Let b be a side of the triangle (all sides are equal in measure)
Altitude / Height = 5 cm
Find the side:
b = [tex]( \frac{2}{ \sqrt{3} } )(h)[/tex]
b = [tex]( \frac{2}{ \sqrt{3} } )(5 cm) [/tex]
b = [tex] \frac{10cm}{ \sqrt{3} } [/tex]
b = [tex] \frac{10cm}{1.73} [/tex]
b = 5.78 cm
B) Solve for the area:
Area of triangle = [tex] \frac{(base)(height)}{2} [/tex]
Area = [tex] \frac{(5.78cm)(5cm)}{2} [/tex]
Area = [tex] \frac{28.9cm ^{2} }{2} [/tex]
Area ≈ 14.45 cm²
ANSWER: The area is 14.45 cm².
