After you break apart a rectangular pyramid, what two-dimensional shapes appear in the net?
triangles
square and triangle
rectangles
rectangle and triangles
triangles
An illustration shows a pyramid with a rectangular base of length l and width w. The perpendicular height, drawn as a dotted line from the apex to the center of the base, is labeled h. The sides that are not visible are drawn in dashed lines.
What is the formula to solve for the slant height of the side triangles in the rectangular pyramid?
=h
=(l2)2 + h2−−−−−−−−−√
=(w2)2 +h2−−−−−−−−−√
=l⋅w
=(l^2 + w^2)^(1/2)
Use the image to answer the question.
An illustration shows a pyramid with a square base. The side of the base is labeled 15 feet. The perpendicular height denoted by a right angle symbol on the lateral face from the apex to the base is labeled 9.9 feet.
Solve for the surface area of the square pyramid.
819 ft.2
522 ft.2
148.5 ft.2
299.25 ft.2
To solve this problem, we first need to find the slant height of the pyramid. We can use the Pythagorean theorem:
slant height = √(height^2 + (1/2*side)^2)
slant height = √(9.9^2 + (1/2*15)^2)
slant height ≈ 10.8 feet
Now we can find the surface area. There are four triangular faces, each with base 15 feet and height 10.8 feet:
4 * (1/2 * base * height) = 4 * (1/2 * 15 * 10.8) = 324
There is also the square base with side length 15 feet:
1 * side^2 = 1 * 15^2 = 225
Adding these areas together, we get:
surface area = 324 + 225 = 549
Therefore, the surface area of the square pyramid is approximately 549 square feet, so the closest answer choice is 522 ft.2.
What is the slant height in a rectangular or square pyramid?
Responses
the height of the pyramid from the apex straight down to the middle of the base of the pyramid
an edge of a triangular face
the distance across the triangular face
the height from the apex straight down to the base of the triangular face where it forms a right angle
the distance across the triangular face.
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 20 centimeters and the width as 18 centimeters. The perpendicular heights from the apex to the base length of 20 is 16.6 centimeters and to the base width of 18 is 17.2 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 of the rectangular pyramid?
1,643.2 cm2
102,787.2 cm2
1,001.6 cm2
1,178.8 cm2
To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.
There are four triangular faces, each with base 18 cm and height 16.6 cm or 17.2 cm:
Area of first triangular face = (1/2 * 18 * 16.6) cm^2 = 149.4 cm^2
Area of second triangular face = (1/2 * 20 * 16.6) cm^2 = 166 cm^2
Area of third triangular face = (1/2 * 18 * 17.2) cm^2 = 155.16 cm^2
Area of fourth triangular face = (1/2 * 20 * 17.2) cm^2 = 172 cm^2
There is also a rectangular base with length 20 cm and width 18 cm:
Area of rectangular base = 20 * 18 = 360 cm^2
Adding all of these areas together, we get:
149.4 + 166 + 155.16 + 172 + 360 = 1002.56
Therefore, the surface area of the rectangular pyramid is approximately 1002.56 cm^2, so the closest answer choice is 1,001.6 cm^2.
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base of length l and width w. The perpendicular height, drawn as a dotted line from the apex to the center of the base, is labeled h. The sides that are not visible are drawn in dashed lines.
What is the formula to solve for the slant height of the side triangles in the rectangular pyramid?