I am to find the area of an equilateral triangle whose side is 5... I know I need to find the highth before I find the area, but I end up with a hight of the square root of 31.25, is this right? if so how do I continue and solve for the area with this kind of number?
Area = 1/2 Base * height
With Pythagorean theorem for half of the triangle to give you the height:
5^2 = 2.5^2 + h^2
25 = 6.25 + h^2
h^2 = 25 - 6.25 = 18.75
Find square root of 18.75 and insert values into the first equation.
I hope this helps.
To find the area of an equilateral triangle, you are correct that you first need to find the height (altitude).
Now, let's determine if your calculation for the height is correct. For an equilateral triangle with a side length of 5, we can use the Pythagorean theorem to find the height.
Since an equilateral triangle is made up of two congruent right-angled triangles, we can split it in half to form a right-angled triangle. In this triangle, the hypotenuse is the side of the equilateral triangle (5), and the height is the side you are looking for.
Using the Pythagorean theorem, we have:
height^2 + (base/2)^2 = side^2
Let's substitute the known values:
height^2 + (5/2)^2 = 5^2
height^2 + 6.25 = 25
height^2 = 25 - 6.25
height^2 = 18.75
At this point, we can use a calculator to find the square root of 18.75. After calculating, we get approximately 4.33.
So, the correct height of the equilateral triangle is approximately 4.33 (rounded to two decimal places).
To calculate the area of the equilateral triangle, we can use the formula:
Area = (1/2) * base * height
Since all sides of an equilateral triangle are equal, the base is also 5. Substituting the values, the formula becomes:
Area = (1/2) * 5 * 4.33
Calculating this, we get:
Area = (1/2) * 5 * 4.33 = 10.825
Therefore, the area of the equilateral triangle with a side length of 5 is approximately 10.825 square units.