Question

Cam's tent (shown below) is a triangular prism. Find the surface area, including the floor, of his tent.

Answer 1

The surface area of the tent is 21.4 m²

Step-by-step explanation:

To find the surface area of a prism you must calculate:

1. The perimeter of the base

2. The area of the base

3. The height of the prism

We have a triangular prism:

Its base is an equilateral triangle of side length 2 m and height 1.7 m

The height of the prism is 3 m

∵ The surface are of the prism is:

   S.A = perimeter of the base × height + 2 × area of the base

∵ The perimeter of the equilateral triangle = 3 × length of a side

∵ The length of the side = 2 m

∴ The perimeter of the base = 3 × 2 = 6 m

∵ The area of the triangle = $\frac{1}{2}$ × base × height

∵ The length of the base of the triangle = 2 m

∵ The height of the triangle = 1.7 m

∴ The area of the base = $\frac{1}{2}$ × 2 × 1.7 = 1.7 m²

∵ S.A = perimeter of the base × height + 2 × area of the base

∵ The perimeter of the base = 6 m

∵ The area of the base = 1.7 m²

∵ The height of the prism = 3 m

∴ S.A = 6 × 3 + 2 × 1.7

∴ S.A = 18 + 3.4

∴ S.A = 21.4 m²

The surface area of the tent is 21.4 m²

Learn more:

You can learn more about surface area of a solid in brainly.com/question/12613605

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Answer 2

We have been given that Cam's tent is a triangular prism. We are asked to find the surface area of Cam's tent including the floor.

The total surface area of tent would be sum of area of all sides.

We can see that two sides of tent are triangular, so their area will be equal to area of triangle.

$\text{Area of 2 triangular sides}=2\times\frac{1}{2} \times \text{Base}\times \text{Height}$

$\text{Area of 2 triangular sides}=2\times\frac{1}{2} \times \text{2 m}\times \text{1.7 cm}$

$\text{Area of 2 triangular sides}=3.4 \text{ m}^2$

Now we can see that tent has two rectangular sides.

$\text{Area of 2 rectangular sides}=2\times \text{Length}\times \text{Width}$

$\text{Area of 2 rectangular sides}=2\times \text{2 m}\times \text{3 m}$

$\text{Area of 2 rectangular sides}=12\text{ m}^2$

We can see that floor of tent is also rectangular.

$\text{Area of floor}=3\text{ m}\times 2\text{ m}$

$\text{Area of floor}=6\text{ m}^2$

$\text{Tent's total area}=3.4\text{ m}^2+12\text{ m}^2+6\text{ m}^2$

$\text{Tent's total area}=21.4\text{ m}^2$

Therefore, the total area of tent is 21.4 square meters.