To find the surface area of the rectangular pyramid, we need to calculate the area of the rectangular base and the area of the three triangular faces.
Area of the rectangular base = length x width
= 8 mm x 10 mm
= 80 mm²
Now, we need to calculate the area of the three triangular faces.
Area of the first triangular face = 1/2 x base x height
= 1/2 x 8 mm x 12 mm
= 48 mm²
Area of the second triangular face = 1/2 x base x height
= 1/2 x 10 mm x 12 mm
= 60 mm²
Area of the third triangular face = 1/2 x base x height
= 1/2 x diagonal x height
= 1/2 x 17 mm x 15 mm
= 127.5 mm²
Now, calculate the total surface area of the rectangular pyramid by adding the area of the base and the three triangular faces:
Total surface area = Area of the rectangular base + Area of the three triangular faces
= 80 mm² + 48 mm² + 60 mm² + 127.5 mm²
= 315.5 mm²
Therefore, the surface area of the rectangular pyramid is 315.5 mm².
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?
(1 point)
mm2
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3 answers
it wasn't right
I apologize for the mistake. Let's calculate the surface area of the rectangular pyramid again.
Since the pyramid has a rectangular base, it consists of one rectangle as the base and four triangles as the lateral faces.
1. Area of the base rectangle:
Area = length x width
Area = 8 mm x 10 mm
Area = 80 mm²
2. Area of the four triangular faces:
Area of each triangular face = 1/2 x base x height
Triangle 1 (with base 8 mm and height 12 mm):
Area = 1/2 x 8 mm x 12 mm
Area = 48 mm²
Triangle 2 (with base 10 mm and height 12 mm):
Area = 1/2 x 10 mm x 12 mm
Area = 60 mm²
Triangle 3 (with base 8 mm and slant height 15 mm):
Area = 1/2 x 8 mm x 15 mm
Area = 60 mm²
Triangle 4 (with base 10 mm and slant height 15 mm):
Area = 1/2 x 10 mm x 15 mm
Area = 75 mm²
3. Calculating the total surface area:
Total Surface Area = Area of base rectangle + Area of four triangular faces
Total Surface Area = 80 mm² + 48 mm² + 60 mm² + 60 mm² + 75 mm²
Total Surface Area = 323 mm²
Therefore, the correct surface area of the rectangular pyramid is 323 mm².
Since the pyramid has a rectangular base, it consists of one rectangle as the base and four triangles as the lateral faces.
1. Area of the base rectangle:
Area = length x width
Area = 8 mm x 10 mm
Area = 80 mm²
2. Area of the four triangular faces:
Area of each triangular face = 1/2 x base x height
Triangle 1 (with base 8 mm and height 12 mm):
Area = 1/2 x 8 mm x 12 mm
Area = 48 mm²
Triangle 2 (with base 10 mm and height 12 mm):
Area = 1/2 x 10 mm x 12 mm
Area = 60 mm²
Triangle 3 (with base 8 mm and slant height 15 mm):
Area = 1/2 x 8 mm x 15 mm
Area = 60 mm²
Triangle 4 (with base 10 mm and slant height 15 mm):
Area = 1/2 x 10 mm x 15 mm
Area = 75 mm²
3. Calculating the total surface area:
Total Surface Area = Area of base rectangle + Area of four triangular faces
Total Surface Area = 80 mm² + 48 mm² + 60 mm² + 60 mm² + 75 mm²
Total Surface Area = 323 mm²
Therefore, the correct surface area of the rectangular pyramid is 323 mm².