When adding polynomials you add the integers in front of like-termed variables raised to the same power.

So in this case we take the numbers and add 

After addition we add the variable  to get 

We have the answer .

When subtracting polynomials you only subtract the integers in front of like-termed variables raised to the same power.

So in this case we take the numbers and subtract them 

After subtraction we add the variable  to get .

The answer is .

When adding variables raised to the same power, add the values in front of the like-termed variables. In this case, we add  and  to get .

When dividing variables raised to the same power, subtract the power of the bottom term from the power of the top term. In this case, subtract  from  to find the power of the answer, .

By definition, an equilateral triangle has three congruent sides. The perimeter is the sum of those sides. Thus, to find the length of just one of those sides, we can divide the perimeter of the triangle by three.

 divided by  is  meters, which is our answer. 

The area of an equilateral triangle is found using the following formula.

 where 

If the area of ABCD is equal to 45, then the perimeter of EFG is equal to x * 1.5 = 45. 45 / 1.5 = 30, so the perimeter of EFG is equal to 30. This means that each side is equal to 10.

The height of the equilateral triangle EFG creates two 30-60-90 triangles, each with a hypotenuse of 10 and a short side equal to 5. We know that the long side of 30-60-90 triangle (here the height of EFG) is equal to √3 times the short side, or 5√3.

We then apply the formula for the area of a triangle, which is 1/2 * b * h. We get 1/2 * 10 * 5√3 = 5 * 5√3 = 25√3.

In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3s/ 2 * s = √3s²/4.

An equilateral triangle has three congruent sides and results in three congruent angles. This figure results in two special right triangles back to back: 30° – 60° – 90° giving sides of x - x √3 – 2x in general. The height of the triangle is the x √3 side.  So A_triangle = 1/2 bh = 1/2 * 12 * 6√3 = 36√3 cm².

To calculate the height, the length of a perpendicular bisector must be determined. If a perpendicular bisector is drawn in an equilateral triangle, the triangle is divided in half, and each half is a congruent 30-60-90 right triangle. This type of triangle follows the equation below.

The length of the hypotenuse will be one side of the equilateral triangle.

.

The side of the equilateral triangle that represents the height of the triangle will have a length of because it will be opposite the 60^o angle.

To calculate the area of the triangle, multiply the base (one side of the equilateral triangle) and the height (the perpendicular bisector) and divide by two.

In order to find the area of the triangle, we must first calculate the height of its altitude.  An altitude slices an equilateral triangle into two  triangles. These triangles follow a side-length pattern. The smallest of the two legs equals  and the hypotenuse equals . By way of the Pythagorean Theorem, the longest leg or .

Therefore, we can find the height of the altitude of this triangle by designating a value for . The hypotenuse of one of the  is also the side of the original equilateral triangle.  Therefore, one can say that  and .

Now, we can calculate the area of the triangle via the formula .