A toy came in a container that is shaped like a triangular prism. How much wrapping paper is needed to wrap the toy? Round your answer to the nearest whole number. Right Triangle
(1 point)
L: 30.5cm
W: 27.9cm
H: 5.1cm
Side Length: 28.4cm
To calculate the surface area of the triangular prism, we need to find the area of each of the three rectangles that make up the prism and add them together.
1. The area of the rectangular base:
A = L * W
A = 30.5cm * 27.9cm
A = 850.95 cm²
2. The area of the other two rectangles:
A = 2 * L * H
A = 2 * 30.5cm * 5.1cm
A = 310.2 cm²
3. The total surface area of the triangular prism:
SA = 2 * (L * W) + 2 * (L * H) + 2 * (W * H)
SA = 2 * 850.95 cm² + 2 * 310.2 cm² + 2 * (27.9cm * 5.1cm)
SA = 1701.9 cm² + 620.4 cm² + 285.3 cm²
SA = 2607.6 cm²
Therefore, approximately 2608 square centimeters of wrapping paper is needed to wrap the toy.
A toy came in a container that is shaped like a triangular prism. How much wrapping paper is needed to wrap the toy? Round your answer to the nearest whole number. Right Triangle
(1 point)
L: 30.5cm
W: 27.9cm
H: 5.1cm
To wrap a triangular prism-shaped toy, we need to find the surface area of the prism, which is made up of three rectangles:
1. The area of the front and back faces (rectangles):
Area = L * H
Area = 30.5cm * 5.1cm
Area = 155.55 cm²
2. The area of the two side faces (rectangles):
Area = W * H
Area = 27.9cm * 5.1cm
Area = 142.29 cm²
3. The area of the top and bottom faces (triangles):
Area = 2 * (1/2 * L * W)
Area = 2 * (1/2 * 30.5cm * 27.9cm)
Area = 2 * (427.95 cm²)
Area = 855.9 cm²
Now, we add up the areas of the three faces to get the total surface area of the triangular prism:
Total Surface Area = 2 * (L * H) + 2 * (W * H) + 2 * (1/2 * L * W)
Total Surface Area = 2 * 155.55 cm² + 2 * 142.29 cm² + 855.9 cm²
Total Surface Area = 311.1 cm² + 284.58 cm² + 855.9 cm²
Total Surface Area = 1,451.58 cm²
Therefore, approximately 1452 square centimeters of wrapping paper is needed to wrap the toy.