Surface Area Unit Test
6 of 156 of 15 Items
Question
Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The visible rectangular face has a width of 5 centimeters and length of 11 centimeters. The sides and edges that are not visible are indicated by dashed lines. The legs of the triangular face are labeled 3 centimeters and 4 centimeters. The hypotenuse shares the same label as the width of the visible rectangular face.
What is the surface area of the triangular prism?
(1 point)
square centimeters
To find the surface area of the triangular prism, we need to calculate the areas of all the faces and then add them up.
Start with the front triangular face. The area of a triangle can be calculated using the formula: (1/2) * base * height. In this case, the base is 5 cm and the height is 4 cm (from the 3-4-5 triangle given). So, the area of the front triangular face is: (1/2) * 5 cm * 4 cm = 10 square cm.
Next, calculate the area of the right rectangular face. The area of a rectangle can be calculated by multiplying the width and length. In this case, the width is 5 cm and the length is 11 cm. So, the area of the right rectangular face is: 5 cm * 11 cm = 55 square cm.
Since there are two identical triangular faces and three identical rectangular faces on a triangular prism, the total surface area is the sum of the areas of all the faces. Therefore, the surface area of the triangular prism is: (2 * 10 square cm) + (3 * 55 square cm) = 20 square cm + 165 square cm = 185 square cm.
Therefore, the surface area of the triangular prism is 185 square centimeters.
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
To find the wrapping paper needed to wrap the toy container, we need to find the total surface area of the triangular prism.
First, calculate the area of the front triangular face. The area of a triangle can be calculated using the formula: (1/2) * base * height. In this case, the base is 27.9 cm and the height is 5.1 cm. So, the area of the front triangular face is: (1/2) * 27.9 cm * 5.1 cm = 71.145 square cm.
Next, calculate the area of the right rectangular face. The area of a rectangle can be calculated by multiplying the width and length. In this case, the width is 27.9 cm and the length is 30.5 cm. So, the area of the right rectangular face is: 27.9 cm * 30.5 cm = 851.95 square cm.
Calculate the other two faces of the triangular prism, which are identical to the right rectangular face. So, the total area of the three rectangular faces is: 3 * 851.95 square cm = 2555.85 square cm.
Since there are two identical triangular faces and three identical rectangular faces, the total surface area is the sum of the areas of all the faces. Therefore, the surface area of the triangular prism is: (2 * 71.145 square cm) + 2555.85 square cm = 142.29 square cm + 2555.85 square cm = 2698.14 square cm.
Rounded to the nearest whole number, the wrapping paper needed to wrap the toy is 2698 square cm.
Surface Area Unit Test
11 of 1511 of 15 Items
Question
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base of length 6 meters and width 2 meters. The perpendicular height from the apex to the center of the base is labeled 8.8 meters. The slant height from the apex to the center of the width of the rectangle is labeled 9 meters. Both heights are drawn as dotted lines. The sides that are not visible are shown in dashed lines.
When finding the surface area of the rectangular pyramid, what dimension will be used to find the height of the triangular sides?(1 point)
m
When finding the surface area of a rectangular pyramid, the dimension used to find the height of the triangular sides is the slant height.
So, in this case, the dimension that will be used to find the height of the triangular sides is the slant height of 9 meters.
Surface Area Unit Test
12 of 1512 of 15 Items
Question
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An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 centimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
What is the surface area of the rectangular pyramid?
(1 point)
cm2
To find the surface area of the rectangular pyramid, we need to calculate the area of each face separately and then sum them up.
1. Front triangular face: Half the base times the height. For the front face with base 14 cm and height 10.6 cm, the area is (1/2) * 14 cm * 10.6 cm = 74.2 cm^2.
2. Back triangular face: Same as the front triangular face. The area of the back face is also 74.2 cm^2.
3. Two side triangular faces: Each face has a base of 12 cm and a height of 10 cm. So, the area of each side triangular face is (1/2) * 12 cm * 10 cm = 60 cm^2. Since there are 2 side faces, the total area of the side faces is 2 * 60 cm^2 = 120 cm^2.
4. Base rectangle: The area of a rectangle is length times width. The length is 14 cm and the width is 12 cm, so the area of the base is 14 cm * 12 cm = 168 cm^2.
Now, add up all the areas: Front face + back face + side faces + base = 74.2 cm^2 + 74.2 cm^2 + 120 cm^2 + 168 cm^2 = 436.4 cm^2.
Therefore, the surface area of the rectangular pyramid is 436.4 cm^2.
Surface Area Unit Test
13 of 1513 of 15 Items
Question
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An illustration shows a three dimensional composite figure formed by a right triangular prism placed on top of a rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 feet and a height of 8 feet. The width of the rectangular prism is 8 feet. The edges of the hidden side face of the right triangular prism align perfectly with the edges of the hidden top face of the rectangular prism. The right triangular prism is aligned to the left of the rectangular prism. The height of the right triangular prism is not shown. The total height of the left side of the figure is 20 feet. The right triangular prism has a width of 8 feet. The hypotenuse side of the right triangular prism has a length of 15 feet.
What is the surface area of the figure?
(1 point)
ft.2
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To find the surface area of the composite figure formed by the right triangular prism on top of the rectangular prism, we need to calculate the areas of all the visible faces and then sum them up.
1. Rectangular Prism:
- Front face: 12 ft (length) * 8 ft (height) = 96 ft^2
- Top face: 12 ft (length) * 8 ft (width) = 96 ft^2
- Right face: 20 ft (height) * 8 ft (width) = 160 ft^2 (since the height is the total height of the composite figure)
2. Right Triangular Prism:
- Front face: Triangle area = (1/2) * base * height = (1/2) * 8 ft (width) * h (height).
Given that the hypotenuse (slant height) is 15 ft, and the height is 20 ft, we can calculate the base using Pythagorean theorem:
base = √(15^2 - 20^2) = √(225 - 400) = √(-175) (which is not a valid length, indicating an error in the provided information)
Therefore, it seems there might be a mistake in the given information, and the calculation cannot be completed as provided. The surface area of the figure cannot be accurately determined without the correct dimensions for the right triangular prism front face's base.