The tent below is similar to a triangular prism. Calculate the surface area of the tent to find the amount of fabric needed to make the tent.
A tent is shaped like a triangular prism. Its bases have a height measuring 4 feet and a base measuring 5 feet. The faces have a length measuring 8 feet and a width measuring 4.75 feet.
Remember to describe each face of the triangle prism
To calculate the surface area of the tent, we need to calculate the area of each individual face and then add them together.
1. Base 1: This is a triangle with base 5 feet and height 4 feet.
Area = 1/2 * base * height
Area = 1/2 * 5 * 4
Area = 10 square feet
2. Base 2: This is identical to Base 1.
Area = 10 square feet
3. Face 1: This is a rectangle with length 8 feet and width 4.75 feet.
Area = length * width
Area = 8 * 4.75
Area = 38 square feet
4. Face 2: This is identical to Face 1.
Area = 38 square feet
5. Face 3: This is the side of the prism which connects the top and bottom bases (rectangles). The height of this face is the same as the height of the prism (4 feet) and the length is the same as the perimeter of the base rectangle (5 + 5 + 8 = 18 feet).
Area = height * length
Area = 4 * 18
Area = 72 square feet
Adding all the areas together:
Total surface area = 10 (Base 1) + 10 (Base 2) + 38 (Face 1) + 38 (Face 2) + 72 (Face 3)
Total surface area = 168 square feet
Therefore, the amount of fabric needed to make the tent is 168 square feet.
What is the formula of a triangular, prism surface area?
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2* (base area) + (lateral area)
Where:
- Base area = area of the two triangular bases
- Lateral area = area of the three rectangular sides
The base area can be calculated using the formula for the area of a triangle: 1/2 * base * height. Since there are two triangular bases in a triangular prism, you multiply this area by 2.
The lateral area can be calculated by finding the perimeter of the base triangle and then multiplying it by the height of the prism.
So, the formula for the surface area of a triangular prism is:
Surface Area = 2 * (1/2 * base * height) + (perimeter of base * height)