An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 30.5 centimeters and 27.9 centimeters. The perpendicular side of the triangular face measures 5.1 centimeter and the hypotenuse measures 28.4 centimeter.
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.
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To calculate the surface area of the triangular prism, we first need to find the area of the three rectangular faces and two triangular faces.
1. Area of the two triangular faces:
Area = 2 * (1/2) * base * height
Area = 2 * (1/2) * 27.9 cm * 5.1 cm
Area = 2 * 13.95 cm * 5.1 cm
Area = 142.695 cm²
2. Area of the three rectangular faces:
The length of the rectangular face is 30.5 cm, and the height is 5.1 cm.
The width of the rectangular face is 27.9 cm, and the height is 5.1 cm.
Area = 2 * [(30.5 cm * 5.1 cm) + (27.9 cm * 5.1 cm)]
Area = 2 * [155.55 cm² + 142.29 cm²]
Area = 2 * 297.84 cm²
Area = 595.68 cm²
3. Total surface area:
Total surface area = Area of two triangles + Area of three rectangles
Total surface area = 142.695 cm² + 595.68 cm²
Total surface area = 738.375 cm²
The amount of wrapping paper needed to wrap the toy would be approximately 738 square centimeters.