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What is the area of an equilateral triangle with side 7? Leave in simplest radical form.

Answer 1

#(49sqrt3)/4#

We can see that if we split an equilateral triangle in half, we are left with two congruent equilateral triangles. Thus, one of the legs of the triangle is #1/2s#, and the hypotenuse is #s#. We can use the Pythagorean Theorem or the properties of #30˚-60˚-90˚# triangles to determine that the height of the triangle is #sqrt3/2s#.

If we want to determine the area of the entire triangle, we know that #A=1/2bh#. We also know that the base is #s# and the height is #sqrt3/2s#, so we can plug those in to the area equation to see the following for an equilateral triangle:

#A=1/2bh=>1/2(s)(sqrt3/2s)=(s^2sqrt3)/4#

Since in your case #s=7#, the area of the triangle is #(7^2sqrt3)/4=(49sqrt3)/4#.

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Answer 2

Maverick Smith

The area of an equilateral triangle with side length (s) is given by the formula (A = \frac{\sqrt{3}}{4} \times s^2). Plugging in (s = 7), we get (A = \frac{\sqrt{3}}{4} \times 7^2 = \frac{\sqrt{3}}{4} \times 49 = \frac{49\sqrt{3}}{4}). So, the area of an equilateral triangle with side length 7 is (\frac{49\sqrt{3}}{4}).

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Answer from HIX Tutor

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