Shaun’s tent (shown below) is a triangular prism. What is the the surface area, including the floor, of his tent?

Shauns tent shown below is a triangular prism What is the the surface area including the floor of his tent class=

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Answer:

The surface area of the ten t including the floor is 52.8 m².

Step-by-step explanation:

We are given that,

Shaun's tent consists of 3 rectangles and 2 triangles.

1. The dimensions of the rectangles are 5 × 3 meters.

Since, Area of the rectangle = Length × Width

i.e. Area of 3 rectangles = 3 × Length × Width

i.e. Area of 3 rectangles = 3 × 5 × 3 = 45 m²

Thus, area of the 3 rectangles is 45 m².

2. The dimensions of the triangles are base= 3 meter and height= 2.6 meter

As, Area of the triangle = [tex]\frac{1}{2}\times Base\times Height[/tex]

i.e. Area of 2 triangles = [tex]2\times \frac{1}{2}\times Base\times Height[/tex]

i.e. Area of 2 triangles = [tex]Base\times Height[/tex]

i.e. Area of 2 triangles = [tex]3\times 2.6[/tex]

i.e. Area of 2 triangles = 7.8 m²

Thus, area of 2 triangles is 7.8 m².

So, the total surface area of the prism = Area of rectangles + Area of triangles

i.e. Total surface area = 45 + 7.8 = 52.8 m²

Hence, the surface area of the ten t including the floor is 52.8 m².

The surface area of the tent including the floor is 52.8 m².

What is the surface area?

The surface area of an object is the total area of the outside surfaces of the three-dimensional object i.e, the total sum of the area of the faces of the object. It is measured in terms of square units.

Shaun's tent consists of 3 rectangles and 2 triangles.

The dimensions of the rectangles are 5 × 3 meters.

Area of the rectangle = Length × Width

Area of 3 rectangles = 3 × Length × Width

Area of 3 rectangles = 3 × 5 × 3 = 45 m²

Thus, the area of the 3 rectangles is 45 m².

The dimensions of the triangles are a base of 3 meters and a height of 2.6 meters.

[tex]\rm Area \ of \ trinagle= 2 \times \dfrac{1}{2} \times base \times height\\\\ Area \ of \ trinagle= 3\times 2.6\\\\ Area \ of \ trinagle= 7.8[/tex]

The surface area, including the floor, of his tent, is;

The total surface area of the prism = Area of rectangles + Area of triangles

Total surface area = 45 + 7.8 = 52.8 m²

Hence, the surface area of the tent including the floor is 52.8 m².

To know more about the surface area click the link given below.

https://brainly.com/question/9930431

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