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?
(1 point)
___ ft.
The pyramid’s height is 12 feet.
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?
(1 point)
ft.
To find the length of the pyramid, we need to use the Pythagorean theorem on the right triangle formed by half the base length (4 ft), half the width (3 ft), and the height of the pyramid (12 ft).
a^2 + b^2 = c^2
(4 ft)^2 + (3 ft)^2 = c^2
16 ft^2 + 9 ft^2 = c^2
25 ft^2 = c^2
c = √25
c = 5 ft
Therefore, the pyramid's length is 5 feet.
Label the parts of the rectangular pyramid with their names.
Enter 1 for apex
Enter 2 for base
Enter 3 for edge
Enter 4 for face
Enter 5 for slant height
(2 points)
1. Apex - Point at the top of the pyramid
2. Base - The rectangular surface at the bottom of the pyramid
3. Edge - The line segment connecting the apex to a point on the base
4. Face - One of the triangular surfaces of the pyramid
5. Slant height - The height of one of the triangular faces of the pyramid
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
To find the surface area of a rectangular pyramid, you can use the formula:
Surface Area = Base Area + (1/2) * perimeter of the base * slant height
First, calculate the base area:
Base Area = length * width
Base Area = 8mm * 10mm = 80 mm^2
Next, calculate the perimeter of the base:
Perimeter of the base = 2 * (length + width)
Perimeter of the base = 2 * (8mm + 10mm) = 36mm
Now, we need to find the slant height. Since it's given that the perpendicular heights to the base length and width are 12mm and 15mm respectively, we can find the slant height using the Pythagorean theorem for the triangles formed by 12mm and half the base length (4mm) for one, and 15mm and half the base width (5mm) for the other:
For the first triangle:
slant height^2 = 12^2 + 4^2
slant height^2 = 144 + 16
slant height^2 = 160
slant height ≈ 12.65 mm
For the second triangle:
slant height^2 = 15^2 + 5^2
slant height^2 = 225 + 25
slant height^2 = 250
slant height ≈ 15.81 mm
Now, calculate the surface area:
Surface Area = 80 + (1/2) * 36 * (12.65 + 15.81)
Surface Area = 80 + 18 * 28.46
Surface Area = 80 + 511.32
Therefore, the surface area of the rectangular pyramid is approximately 591.32 mm^2.
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
To find the surface area of the rectangular pyramid, you have to calculate the areas of the base and the four triangular faces separately and then add them up.
1. Calculate the Base Area:
Base Area = Length x Width
Base Area = 8 mm x 10 mm = 80 mm^2
2. Calculate the Lateral Face Areas:
There are four triangular faces in the pyramid.
For the face with a perpendicular height of 12 mm (related to the base length):
Face Area = (1/2) x Base Length x Perpendicular Height
Face Area = (1/2) x 8 mm x 12 mm = 48 mm^2
For the face with a perpendicular height of 15 mm (related to the base width):
Face Area = (1/2) x Base Width x Perpendicular Height
Face Area = (1/2) x 10 mm x 15 mm = 75 mm^2
3. Calculate Total Surface Area:
Total Surface Area = Base Area + 4 x Face Area
Total Surface Area = 80 mm^2 + 4 x (48 mm^2 + 75 mm^2)
Total Surface Area = 80 mm^2 + 4 x 123 mm^2
Total Surface Area = 80 mm^2 + 492 mm^2
Total Surface Area = 572 mm^2
Therefore, the surface area of the rectangular pyramid is 572 mm^2.
After you break apart a rectangular pyramid, what two-dimensional shapes appear in the net?(1 point)
Responses
square and triangle
square and triangle
triangles
triangles
rectangles
rectangles
rectangle and triangles