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 and sum them up.
1. Base face: The base of the tent is a triangle with a base measuring 5 feet and a height of 4 feet. The formula for the area of a triangle is A = 1/2 * base * height. Plugging in the values, we get A = 1/2 * 5 * 4 = 10 square feet.
2. Front and back faces: These faces are rectangles with a length of 8 feet and a width of 4.75 feet. The formula for the area of a rectangle is A = length * width. Plugging in the values, we get A = 8 * 4.75 = 38 square feet.
3. Side faces: There are two side faces of the triangular prism, each with a length of 8 feet and a height of 4 feet (the same as the base face). Similarly to the base face, the formula for the area of a triangle is A = 1/2 * base * height. Plugging in the values, we get A = 1/2 * 8 * 4 = 16 square feet for each side face. Since there are two side faces, the total area for the side faces is 2 * 16 = 32 square feet.
Now, we can sum up the areas of all the faces: 10 (base) + 38 (front and back faces) + 32 (side faces) = 80 square feet.
Therefore, the amount of fabric needed to make the tent is 80 square feet.
can you summarize that please
To determine the surface area of the triangular prism tent, you would calculate the areas of each face:
- Base face: A triangle with a base of 5 feet and height of 4 feet
- Front and back faces: Rectangles with length of 8 feet and width of 4.75 feet
- Side faces: Triangles with length of 8 feet and height of 4 feet
You would use the formulas for area of triangle and rectangle to calculate the areas of each face, then sum them up to find the total surface area, which in this case is 80 square feet. This would give you the amount of fabric needed to make the tent.