Use the image to answer the question.
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.
(1 point)
S.A. =
cm2
SHOW YOUR WORK!!!
To find the surface area of the triangular prism, we need to calculate the area of all the faces and add them together.
1. The area of the triangular face:
A = 1/2 * base * height
A = 1/2 * 27.9 * 5.1
A = 71.145 cm2
2. The areas of the two parallel rectangular faces:
Area = base * height
Area = 30.5 * 5.1
Area = 155.55 cm2
Now add all the areas together to find the total surface area:
Total Surface Area = 2 * (Area of rectangular face) + (Area of triangular face)
Total Surface Area = 2 * 155.55 + 71.145
Total Surface Area = 311.1 + 71.145
Total Surface Area ≈ 382.25 cm2
Therefore, approximately 382 cm2 of wrapping paper is needed to wrap the toy.