The lateral area of the right regular triangular prism is 18 cm^2.Find the total surface area.give your answer in decimal form rounded of to 2 decimal places

Can't tell. The two bases are equilateral triangles, but the three lateral faces are rectangles of area 6. But is the prism tall and skinny, or short and fat?

You must know either the height of the prism, or the side length of its bases.

If the bases are of side 2s, then each base has area √3 s^2.

Now, go complete the calculation.

Tall and skinny..I found out the base of the triangle is 2.

Find the volume of the given project in order to determine the number of feet of concrete needed. Round answers to the nearest whole number when necessary.

A driveway that is 30 feet long, 18 feet wide, and 4 inches thick

To find the total surface area of a right regular triangular prism, we need to consider the lateral area and the bases.

The lateral area of a triangular prism is found by multiplying the perimeter of the base triangle by the height of the prism.
Given that the lateral area is 18 cm^2, we can set up an equation as follows:

Lateral Area = perimeter of base triangle x height
18 cm^2 = (perimeter of base triangle) x (height)

Now, let's consider the base triangle of the triangular prism. Since it is a right regular triangular prism, it means that all sides of the base triangle are equal, and the angles opposite the equal sides are 90 degrees.

Let's say the side length of the triangle is "a." Therefore, the perimeter of the base triangle is 3a.

From here, we can rewrite the equation as:

18 cm^2 = 3a x height (Equation 1)

To find the total surface area, we need to consider both the lateral area and the base area.
The base area of a regular triangular prism is given by:

Base Area = (sqrt(3) x a^2)/4

Since we have three faces contributing to the base area, the total base area is:

3 x Base Area = 3 x (sqrt(3) x a^2)/4

To get the total surface area, we add the lateral area and the base area:

Total Surface Area = Lateral Area + 3 x Base Area
= 18 cm^2 + 3 x (sqrt(3) x a^2)/4

Now, let's solve for "a" by substituting the value of height from Equation 1:

18 cm^2 = 3a x height
18 cm^2 = 3a x (18/3a)
18 cm^2 = 18 cm^2

This indicates that "a" can take any value. However, since we need to calculate the total surface area, we will assume a value.

Let's assume a value of "a" as 3 cm. Now we can calculate the total surface area:

Total Surface Area = 18 cm^2 + 3 x (sqrt(3) x (3 cm)^2)/4

Calculating further gives us:

Total Surface Area = 18 cm^2 + 3 x (sqrt(3) x 9 cm^2)/4
= 18 cm^2 + 3 x (sqrt(3) x 9 cm^2)/4
= 18 cm^2 + 3 x (sqrt(3) x 9 cm^2)/4
= 18 cm^2 + 3 x (3 x 3 x sqrt(3) cm^2)/4
= 18 cm^2 + 81sqrt(3) cm^2)/4

Now, to get the answer in decimal form, we can plug the equation into a calculator considering the value of sqrt(3) as 1.732.
Using a calculator, we find:

Total Surface Area ≈ 18 + (81 x 1.732) / 4
≈ 18 + 140.148 / 4
≈ 18 + 140.148 / 4
≈ 18 + 35.037
≈ 53.037

Rounding the answer to two decimal places:

Total Surface Area ≈ 53.04 cm^2