After you break apart a rectangular pyramid, what two-dimensional shapes appear in the net?(1 point)
Responses
rectangle and triangles
rectangle and triangles
rectangles
rectangles
triangles
triangles
square and triangle
square and triangle
rectangles and triangles
A rectangular pyramid is shown. The base of the pyramid has length labeled l and w. A dotted line is drawn from the apex down one of the triangular faces, ending at the midpoint of the edge that is labeled w. This dotted line is labeled slant height. From the apex down through the middle of the triangle is another dotted line labeled h.
What is the formula to solve for the slant height of the side triangles in the rectangular pyramid?
(1 point)
Responses
=(w/2)2 +h2−−−−−−−−−√
=(l/2)2 + h2−−−−−−−−−√
=h
=l⋅w
=(w/2)^2 + h^2 √
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.
(1 point)
Responses
148.5 ft.2
148.5 ft. squared
522 ft.2
522 ft. squared
299.25 ft.2
299.25 ft. squared
819 ft.2
819 ft. squared
To find the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces, and then sum them up.
Area of the base = side^2 = 15^2 = 225 square feet
Area of each triangular face = (1/2) * base * height = (1/2) * 15 * 9.9 = 74.25 square feet
There are four triangular faces, so total area of all four faces = 4 * 74.25 = 297 square feet
Total surface area = base area + sum of areas of all four faces = 225 + 297 = 522 square feet
Therefore, the surface area of the square pyramid is 522 ft².
So the correct response is:
522 ft.²
What is the slant height in a rectangular or square pyramid?(1 point)
Responses
the distance across the 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 height from the apex straight down to the base of the triangular face where it forms a right angle
the height of the pyramid from the apex straight down to the middle of the base of the pyramid
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
an edge of a triangular face
the distance across the triangular face
A factory makes nylon tea bags. The bags are in the shape of a triangular pyramid. How much nylon is needed to make 50 tea bags given the following dimensions?
Base of the equilateral triangles: 40 mm
Height of the base triangle: 35 mm
Slant height of the equilateral triangular faces: 45 mm
(1 point)
Responses
153,125 mm2
170,000 mm2
3,400 mm2
3,062.5 mm2
To find the total amount of nylon needed to make 50 tea bags, you first need to calculate the lateral surface area of one triangular pyramid and then multiply it by 50.
The lateral surface area of a triangular pyramid is given by the formula:
Lateral Surface Area = (1/2) * Perimeter of the Base * Slant Height
First, calculate the perimeter of the equilateral triangle base:
Perimeter of an equilateral triangle = 3 * side length
Given side length of equilateral triangle = 40 mm
Perimeter = 3 * 40 = 120 mm
Now, calculate the lateral surface area of one pyramid:
Lateral Surface Area = (1/2) * 120 * 45 = 2700 mm²
To find the nylon needed for 50 tea bags:
Total Nylon Needed = 50 * 2700 = 135,000 mm²
Therefore, the correct response is: 135,000 mm²