Surface Area of Rectangular Pyramids Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base of length 8 feet and width 6 feet. The perpendicular height, drawn as a dotted line from the apex to the center of the base, is labeled 12 feet. The sides that are not visible are drawn in dashed lines.
What is the pyramid’s height?
To calculate the surface area of a rectangular pyramid, you need to find the area of the base and the area of the three triangular faces.
1. Start by finding the area of the base:
Area of the base = length x width = 8 mm x 10 mm = 80 mm²
2. Next, find the area of the three triangular faces. Since the pyramid has a rectangular base, the two lateral faces will have a different height:
a. Area of one lateral face = (1/2) x base x height = (1/2) x 8 mm x 12 mm = 48 mm²
b. Area of the other lateral face = (1/2) x base x height = (1/2) x 10 mm x 15 mm = 75 mm²
3. Calculate the total surface area of the pyramid:
Total Surface Area = Area of Base + 2 x Area of Lateral Faces
Total Surface Area = 80 mm² + 48 mm² + 75 mm² = 203 mm²
Therefore, the surface area of the rectangular pyramid is 203 square millimeters.
The pyramid's height is 12 feet, as indicated in the illustration.
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base of length 8 feet and width 6 feet. The perpendicular height, drawn as a dotted line from the apex to the center of the base, is labeled 12 feet. The sides that are not visible are drawn in dashed lines.
What is the pyramid’s length?
The pyramid's length is 8 feet, as indicated by the length of the rectangular base in the illustration.
Surface Area of Rectangular Pyramids Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is 8 millimeters and the width 10 millimeters. The perpendicular heights from the apex to the base length is 12 millimeters and to the base width is 15 millimeters. 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?
wrong
wrong🙄
its not 314 or 203 dont say 203 or 314 😡😠🤬
I apologize for the errors in my previous responses. Let's reevaluate the calculation for the surface area of the rectangular pyramid with the given dimensions.
Given:
Base length = 8 mm
Base width = 10 mm
Height to base length = 12 mm
Height to base width = 15 mm
To find the surface area of the rectangular pyramid, follow these steps:
1. Calculate the base area:
Base Area = length x width = 8 mm x 10 mm = 80 mm²
2. Calculate the lateral surface area of the pyramid:
Lateral Surface Area = (1/2) x Perimeter of Base x Slant Height
First, find the perimeter of the base:
Perimeter = 2(length) + 2(width) = 2(8 mm) + 2(10 mm) = 16 mm + 20 mm = 36 mm
Next, find the slant height:
For the face with height 12 mm, slant height = sqrt(12^2 + (10/2)^2) = sqrt(144 + 25) = sqrt(169) = 13 mm
For the face with height 15 mm, slant height = sqrt(15^2 + (8/2)^2) = sqrt(225 + 16) = sqrt(241) ≈ 15.52 mm
Now, calculate the lateral surface area for both faces:
Lateral Surface Area = (1/2) x Perimeter x Slant Height
For the face with height 12 mm: (1/2) x 36 mm x 13 mm ≈ 234 mm²
For the face with height 15 mm: (1/2) x 36 mm x 15.52 mm ≈ 279.36 mm²
3. Total surface area:
Total Surface Area = Base Area + Sum of Lateral Surface Areas
Total Surface Area = 80 mm² + 234 mm² + 279.36 mm² ≈ 593.36 mm²
Therefore, the surface area of the rectangular pyramid is approximately 593.36 square millimeters. Thank you for your patience, and I appreciate your attention to this matter.
I apologize for my mistake. Let's try calculating the surface area again.
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
1. Base area = length x width = 8 mm x 10 mm = 80 mm²
2. Perimeter of the base:
Perimeter = 2(length + width) = 2(8 mm + 10 mm) = 2(18) = 36 mm
3. Slant Height of one of the triangular faces:
Using the Pythagorean theorem, we can find the slant height of one of the triangular faces:
Slant Height = sqrt((height)^2 + (width/2)^2) = sqrt((12 mm)^2 + (5 mm)^2) = sqrt(144 + 25) = sqrt(169) = 13 mm
4. Calculate the surface area:
Surface Area = 80 mm² + (0.5 x 36 mm x 13 mm)
Surface Area = 80 mm² + (0.5 x 468 mm²)
Surface Area = 80 mm² + 234 mm²
Surface Area = 314 mm²
Therefore, the surface area of the rectangular pyramid is 314 square millimeters. Apologies for the confusion earlier. Thank you for your patience.