The height of an equilateral triangle is 10. Find its area divided by three at the root of the fractional bar three

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Willie Gilmore · Accepted Answer

S tr. = (a h) / 2, where h = height, and is the base of the triangle. (For an equilateral triangle, a is any side.)We have h = 10 cm.Let&#039;s find a. The triangle is equilateral by condition, the height divides it into 2 right-angled triangles, the hypotenuse of which is equal to a, one leg is the height h = 10 cm, and the other = a / 2, (since the height is both the bisector and the median).According to the Pythagorean theorem:       a          2        =      h          2        +  (  a      /    2      )          2        ;  (  4      a          2        )      /    4  =  (  4      h          2        +      a          2        )      /    4  ;  4      a          2        −      a          2        =  4      h          2        ,  3      a          2        =  4      h          2        ;  a  =      4          h              2                    /        3    =  2  h      /        3    ;  a  =  2  ∗  10      /        3    (  c  m  )Let&#039;s find S.   S  =  (  a  ∗  h  )      /    2  =  (  2  ∗  h      /        3    )  ∗  h      /    2  =      h          2            /        3    ;  S  =  10  ∗  10      /        3    (  c      m          2        )Let&#039;s find   S  :  (      3          /        3    )  S  :  (      3          /        3    )  =  (      h          2            /        3    )  :  (      3          /        3    )  =  (      h          2        ∗  3  )      /    (      3    ∗      3    )  =      h          2        =  10  ∗  10  =  100  (  c      m          2        )Answer:   S  :  (      3          /        3    )  =  100  c      m          2

The height of an equilateral triangle is 10. Find its area divided by three at the root of the fractional bar three

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