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The altitude of an equilateral triangle is the square root of 3 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.

 Sep 29, 2020
 #1
avatar+10336 
+1

The altitude of an equilateral triangle is the square root of 3 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.

 

Hello Guest!

 

\(A=\frac{1}{2}ah\)

\(h=\sqrt{3}\)

 

\(a^2=(\frac{a}{2})^2+h^2\\ a^2-\frac{a^2}{4}=h^2\)

\(\frac{3}{4}a^2=3\\ a=\sqrt{\frac{3\cdot 4}{3}}\)

\(a=2\)

\(A=\frac{1}{2}ah\)

\(A=\frac{1}{2}\cdot 2\cdot \sqrt{3}\)

\(A=\sqrt{3}\)

laugh  !

 Sep 29, 2020
 #2
avatar+27778 
0

You lost me on this one, asinus.....

    can you explain this step? :

a^2 = (a/2)^2 + h^2         won't that just give you the side length and not the base length?  

                                              Seems to me that we need more info to solve this Q   blush

 Sep 29, 2020
 #3
avatar+27778 
+1

   SORRY .... I see your answer method now !   I read the question incorrectly as an isosceles triangle rather than equilateral triangle ....     D'Oh !

ElectricPavlov  Sep 29, 2020
edited by ElectricPavlov  Sep 29, 2020

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