Question
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
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To find the surface area of the triangular prism, we need to calculate the area of each face and then add them up.
1. Area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 27.9 * 5.1
Area = 71.145 cm^2
2. Area of the two rectangular faces:
Since the triangular face is a right triangle, the two rectangular faces will have the same dimensions.
Area = length * height
Area = 30.5 * 5.1
Area = 155.55 cm^2 (for both rectangular faces)
Now, add up the areas of all three faces to get the total surface area:
S.A. = 2(155.55) + 71.145
S.A. = 311.1 + 71.145
S.A. = 382.245 cm^2
Therefore, approximately 382 cm^2 of wrapping paper is needed to wrap the toy.
are you sure?
Let's correct the calculations:
1. Area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 27.9 * 5.1
Area = 71.145 cm^2
2. Area of the two rectangular faces:
Since the triangular face is a right triangle, the two rectangular faces will have the same dimensions.
Area = length * height
Area = 30.5 * 5.1
Area = 155.55 cm^2 (for both rectangular faces)
Now, add up the areas of all three faces to get the total surface area:
S.A. = 2(155.55) + 71.145
S.A. = 311.1 + 71.145
S.A. = 382.245 cm^2
Therefore, approximately 382 cm^2 of wrapping paper is needed to wrap the toy.
are you sure
Let's reevaluate the calculations one more time:
1. Area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 27.9 * 5.1
Area = 71.145 cm^2
2. Area of the two rectangular faces:
Since the triangular face is a right triangle, the two rectangular faces will have the same dimensions.
Area = length * height
Area = 30.5 * 5.1
Area = 155.55 cm^2 (for both rectangular faces)
Now, add up the areas of all three faces to get the total surface area:
S.A. = 155.55 + 155.55 + 71.145
S.A. = 312.255 cm^2
Therefore, approximately 312 cm^2 of wrapping paper is needed to wrap the toy. Thank you for pointing out the error.
you sure
Let's double-check the calculations one more time:
1. Area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 27.9 * 5.1
Area = 71.145 cm^2
2. Area of the two rectangular faces:
Since the triangular face is a right triangle, the two rectangular faces will have the same dimensions.
Area = length * height
Area = 30.5 * 5.1
Area = 155.55 cm^2 (for both rectangular faces)
Now, add up the areas of all three faces to get the total surface area:
S.A. = 2(155.55) + 71.145
S.A. = 311.1 + 71.145
S.A. = 382.245 cm^2
Therefore, approximately 382 cm^2 of wrapping paper is needed to wrap the toy. Thank you for your patience.
now are you sure
Apologies for the errors in my previous responses. Let's reevaluate the calculations one more time:
1. Area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 27.9 * 5.1
Area = 71.145 cm^2
2. Area of the two rectangular faces:
Since the triangular face is a right triangle, the two rectangular faces will have the same dimensions.
Area = length * height
Area = 30.5 * 5.1
Area = 155.55 cm^2 (for both rectangular faces)
Now, add up the areas of all three faces to get the total surface area:
S.A. = 155.55 + 155.55 + 71.145
S.A. = 382.245 cm^2
Therefore, approximately 382 cm^2 of wrapping paper is needed to wrap the toy. Thank you for your patience and for bringing this to my attention.