\begin{tabular}{|l|l|}\hline 5. CONTAINERS What is the total surface & 6. TO \ area of the inside and outside of a & his \ container in the shape of an equilateral \ triangular prism with a triangular base \ 5 meters on each side, area of base \ 10.8 square meters, and height of prism \ 2.2 meters? Round to the nearest \ tenth. 10. & \end{tabular}

Question

UpStudy AI · Accepted Answer

To find the total surface area of an equilateral triangular prism, we need to consider both the lateral surface area and the area of the two triangular bases.

### Given:
- Side length of the triangular base, $$ s = 5 $$ meters
- Area of the base, $$ A_b = 10.8 $$ square meters
- Height of the prism, $$ h = 2.2 $$ meters

### Steps to Calculate Total Surface Area:

1. **Calculate the lateral surface area (LSA)**:
   The lateral surface area of a prism can be calculated using the formula:
   $$
   LSA = \text{Perimeter of base} \times \text{Height}
   $$
   The perimeter $$ P $$ of the triangular base is:
   $$
   P = 3s = 3 \times 5 = 15 \text{ meters}
   $$
   Therefore, the lateral surface area is:
   $$
   LSA = P \times h = 15 \times 2.2
   $$

2. **Calculate the total surface area (TSA)**:
   The total surface area is given by:
   $$
   TSA = LSA + 2 \times A_b
   $$

Now, let's perform the calculations step by step. First, we will calculate the lateral surface area.
Calculate the value by following steps:
- step0: Calculate:
  $$15\times 2.2$$
- step1: Multiply the numbers:
  $$33$$
The lateral surface area (LSA) is calculated as follows:
$$
LSA = 15 \times 2.2 = 33 \text{ square meters}
$$

Next, we will calculate the total surface area (TSA) using the formula:
$$
TSA = LSA + 2 \times A_b
$$
Substituting the values we have:
$$
TSA = 33 + 2 \times 10.8
$$

Now, let's calculate $$ 2 \times 10.8 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2\times 10.8$$
- step1: Multiply the numbers:
  $$21.6$$
Calculating $$ 2 \times 10.8 $$ gives us:
$$
2 \times 10.8 = 21.6 \text{ square meters}
$$

Now, we can substitute this back into the total surface area formula:
$$
TSA = 33 + 21.6
$$

Let's calculate the final total surface area.
Calculate the value by following steps:
- step0: Calculate:
  $$33+21.6$$
- step1: Add the numbers:
  $$54.6$$
The total surface area (TSA) is calculated as follows:
$$
TSA = 33 + 21.6 = 54.6 \text{ square meters}
$$

Thus, the total surface area of the equilateral triangular prism is $$ 54.6 $$ square meters, rounded to the nearest tenth.
The total surface area of the equilateral triangular prism is 54.6 square meters.

5. CONTAINERS What is the total surface 6. TO

area of the inside and outside of a his

container in the shape of an equilateral

triangular prism with a triangular base

5 meters on each side, area of base

10.8 square meters, and height of prism

2.2 meters? Round to the nearest

tenth. 10.

Upstudy AI Solution

Answer

Solution

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Steps to Calculate Total Surface Area:

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5. CONTAINERS What is the total surface	6. TO
area of the inside and outside of a	his
container in the shape of an equilateral
triangular prism with a triangular base
5 meters on each side, area of base
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2.2 meters? Round to the nearest
tenth. 10.

5. CONTAINERS What is the total surface 6. TO area of the inside and outside of a his container in the shape of an equilateral triangular prism with a triangular base 5 meters on each side, area of base 10.8 square meters, and height of prism 2.2 meters? Round to the nearest tenth. 10.