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.
(2 points)
To determine the surface area of the tent, we need to calculate the area of each face of the triangular prism.
1. The two triangular faces: Each triangular face of the prism is a right triangle with a base of 5 feet and a height of 4 feet. The area of a triangle is calculated using the formula:
Area = 1/2 * base * height
For each triangular face:
Area = 1/2 * 5 * 4
Area = 10 square feet
Since there are two triangular faces, the total area of the two triangular faces is:
Total area of triangular faces = 2 * 10 square feet
Total area of triangular faces = 20 square feet
2. The three rectangular faces: Each rectangular face of the prism has a length of 8 feet and a width of 4.75 feet. The area of a rectangle is calculated as:
Area = length * width
For each rectangular face:
Area = 8 * 4.75
Area = 38 square feet
Since there are three rectangular faces, the total area of the three rectangular faces is:
Total area of rectangular faces = 3 * 38 square feet
Total area of rectangular faces = 114 square feet
To find the total surface area of the tent, we add the total area of the triangular faces and the total area of the rectangular faces:
Total surface area = Total area of triangular faces + Total area of rectangular faces
Total surface area = 20 square feet + 114 square feet
Total surface area = 134 square feet
Therefore, the amount of fabric needed to make the tent would be 134 square feet.