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find the area of an equilateral triangle if its altitude is 5cm

Sagot :

si quelateral means all sides are equal given ABC 
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.