What is the area of an equilateral triangle with a side length of 5?

Answer 1

#(25sqrt3)/4#

We can see that if we split an equilateral triangle in half, we are left with two congruent right triangles. Thus, one of the legs of one of the right triangles 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#

In your case, #s=5#, so the area equals:

#(5^2sqrt3)/4=(25sqrt3)/4#

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Answer 2

Aaliyah Anderson

The area of an equilateral triangle with a side length of 5 units is approximately 10.83 square units.

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Answer 3

Sophia Alfred

The area of an equilateral triangle with a side length of 5 units is approximately 10.83 square units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.