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.
the tent below is 4.75ft 4ft. 5ft and 8ft
To find the surface area of the triangular prism tent, we first need to calculate the area of each face.
1. Base Triangle: The base of the tent is a triangle with sides measuring 4 feet, 5 feet, and 8 feet. To find the area of this triangle, we can use Heron's formula:
s = (4 + 5 + 8) / 2 = 8.5
Area = √[8.5 * (8.5 - 4) * (8.5 - 5) * (8.5 - 8)] = √[8.5 * 4.5 * 3.5 * 0.5] = √(66.375) ≈ 8.15 sq. ft.
2. Rectangular Faces: The triangular prism tent has two rectangular faces - one with dimensions 4.75ft x 8ft and one with dimensions 4.75ft x 5ft. To find the area of each rectangle, we multiply the length by the width:
Area of Rectangle 1 = 4.75 * 8 = 38 sq. ft.
Area of Rectangle 2 = 4.75 * 5 = 23.75 sq. ft.
Now, the total surface area of the triangular prism tent can be calculated by adding the areas of all the faces:
Total Surface Area = 2 * (Area of Base Triangle) + 2 * (Area of Rectangle 1) + 2 * (Area of Rectangle 2)
Total Surface Area = 2 * 8.15 + 2 * 38 + 2 * 23.75
Total Surface Area = 16.3 + 76 + 47.5
Total Surface Area = 139.8 sq. ft.
Therefore, approximately 139.8 square feet of fabric would be needed to make the tent.