The tent below is shaped like a triangular prism. EXPLAIN how you would determine the surface area of the tent to find the amount of fabric needed to make the tent. Remember to describe each face of the triangular prism.
Georgia Milestones Grade 7 Mathematics Formula Sheet
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.
To determine the surface area of the tent, you would first calculate the surface area of each face of the triangular prism. The tent has three rectangular faces and two triangular faces.
- The two triangular faces: To find the area of a triangle, you would use the formula A = 0.5 * base * height. In this case, the base is 5 feet and the height is 4 feet. So for each triangular face, the area would be 0.5 * 5 * 4 = 10 square feet.
- The three rectangular faces: To find the area of a rectangle, you would use the formula A = length * width. In this case, the length is 8 feet and the width is 4.75 feet. So for each rectangular face, the area would be 8 * 4.75 = 38 square feet.
To find the total surface area of the tent, you would add up the areas of all five faces. So the total surface area would be:
2 (triangular faces) + 3 (rectangular faces) = 2 * 10 + 3 * 38 = 20 + 114 = 134 square feet.
Therefore, you would need 134 square feet of fabric to make the tent.
is this correct?
Apologies for the confusion in my previous response. Let's clarify the calculation of the surface area of the tent shaped like a triangular prism.
1. Triangular Faces:
The tent has two triangular faces. Each face is a right-angled triangle with base 5 feet and height 4 feet.
Area of one triangular face = 0.5 * base * height
Area of one triangular face = 0.5 * 5 * 4
Area of one triangular face = 10 square feet
Since there are two triangular faces, the total area of the triangular faces is:
2 * 10 = 20 square feet
2. Rectangular Faces:
The tent has three rectangular faces. Each face has a length of 8 feet and a width of 4.75 feet.
Area of one rectangular face = length * width
Area of one rectangular face = 8 * 4.75
Area of one rectangular face = 38 square feet
Since there are three rectangular faces, the total area of the rectangular faces is:
3 * 38 = 114 square feet
3. Total Surface Area:
Total surface area of the tent = Total area of triangular faces + Total area of rectangular faces
Total surface area = 20 + 114
Total surface area = 134 square feet
Therefore, the correct amount of fabric needed to make the tent is 134 square feet. Thank you for your patience, and I appreciate your attention to detail.