The formula for the area of a right triangle is , where is the length of the triangle's base and is its height. Since the longest side is the hypotenuse, use the two smaller numbers given as sides for the base and height in the equation to calculate the area of Triangle A:

The formula for the area of an equilateral triangle is , where is the length of each side. (Alternatively, you can divide the equilateral triangle into two right triangles and find the area of each). Triangle B's area is thus calculated as:

To determine which of the two areas is greater without using a calculator, rewrite the areas of the two triangles with comparable factors. Triangle A's area can be expressed as , and Triangle B's area can be expressed as . Since is greater than , the product of the factors of Triangle B's area will be greater than the product of the factors of Triangle A's, so Triangle B has the greater area.

When you draw the height in an equilateral triangle, it makes two 30-60-90 triangles. Because of that relationship, the height (which is across from the ) is .

When you draw the height in an equilateral triangle, it makes two 30-60-90 triangles. Because of that relationship, the height (which is across from the ) is .

The formula for the area of a right triangle is , where is the length of the triangle's base and is its height. Since the longest side is the hypotenuse, use the two smaller numbers given as sides for the base and height in the equation to calculate the area of Triangle A:

The formula for the area of an equilateral triangle is , where is the length of each side. (Alternatively, you can divide the equilateral triangle into two right triangles and find the area of each). Triangle B's area is thus calculated as:

To determine which of the two areas is greater without using a calculator, rewrite the areas of the two triangles with comparable factors. Triangle A's area can be expressed as , and Triangle B's area can be expressed as . Since is greater than , the product of the factors of Triangle B's area will be greater than the product of the factors of Triangle A's, so Triangle B has the greater area.

The formula for the perimeter of an equilateral triangle is:

Plugging in our values, we get

The formula for the area of an equilateral triangle is:

Plugging in our values, we get

Since the area of a triangle is

you need to find the height of the triangle first. Because of the 30-60-90 relationship, you can determine that the height is .

Then, multiply that by the base (11).

Finally, divide it by two to get 52.4.

If we draw a line segment between X and the base of the triangle, we form a triangle.

We can use the relationships between the sides of a triangle in order to find the length of X.

We know the base opposite the is .

The value of the height opposite the must then be , or .

Therefore, the value of X will be twice the value of the height:

If we draw a line segment between X and the base of the triangle, we form a triangle.

We can use the relationships between the sides of a triangle in order to find the length of X.

We know the base opposite the is .

The value of the height opposite the must then be , or .

Therefore, the value of X will be twice the value of the height:

The formula for the perimeter of an equilateral triangle is:

Plugging in our values, we get

The formula for the area of an equilateral triangle is:

Plugging in our values, we get

Since the area of a triangle is

you need to find the height of the triangle first. Because of the 30-60-90 relationship, you can determine that the height is .

Then, multiply that by the base (11).

Finally, divide it by two to get 52.4.