After you break apart a rectangular pyramid, what two-dimensional shapes appear in the net?(1 point)
Responses
rectangles
rectangles
triangles
triangles
rectangle and triangles
rectangle and triangles
square and triangle
rectangle and triangles
Use the image to answer the question.
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
=(w2)2 +h2−−−−−−−−−√
equals Start Root left parenthesis Start Fraction w over 2 End Fraction right parenthesis squared plus h squared End Root
=(l2)2 + h2−−−−−−−−−√
equals Start Root left parenthesis Start Fraction l over 2 End Fraction right parenthesis squared plus h squared End Root
=h
equals h
=l⋅w
=√(w/2)^2 + h^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.
(1 point)
Responses
522 ft.2
522 ft. squared
819 ft.2
819 ft. squared
299.25 ft.2
299.25 ft. squared
148.5 ft.2
To find the surface area of a square pyramid, we need to calculate the area of the base (which is a square) and the areas of the four triangular faces.
Given:
Base side length = 15 feet
Height of pyramid = 9.9 feet
To find the base area:
Area of a square = side length^2
Area = 15^2 = 225 square feet
To find the area of each triangular face:
Each triangle has a base equal to the base side length of the square (15 feet) and a height equal to the height of the pyramid (9.9 feet).
Area of a triangle = (1/2) * base * height
Area = 0.5 * 15 * 9.9 = 74.25 square feet
Since the pyramid has 4 triangular faces, the total area of the four triangular faces is:
4 * 74.25 = 297 square feet
Therefore, the total surface area of the square pyramid is the sum of the base area and the four triangular face areas:
225 (base) + 297 (triangular faces) = 522 square feet
Therefore, the correct response is:
522 ft.2
What is the slant height in a rectangular or square pyramid?(1 point)
Responses
an edge of a triangular face
an edge of a triangular face
the distance across the triangular face
the distance across the triangular face
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
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
e 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 point)
Responses
1,178.8 cm2
1,178.8 cm squared
1,001.6 cm2
1,001.6 cm squared
1,643.2 cm2
1,643.2 cm squared
102,787.2 cm2
To find the surface area of a rectangular pyramid, we calculate the area of the rectangular base and the areas of the four triangular faces.
Given:
Length of the base = 20 cm
Width of the base = 18 cm
Height from the apex to the base length of 20 cm = 16.6 cm
Height from the apex to the base width of 18 cm = 17.2 cm
To find the base area:
Area of a rectangle = length * width
Base area = 20 * 18 = 360 square cm
To find the area of each triangular face:
Area of a triangle = (1/2) * base * height
The heights provided are the slant heights of the triangles. We need to calculate the base of each triangle using the Pythagorean Theorem:
For the height of 16.6 cm:
Base of triangle = √(20/2)^2 + 16.6^2 = √100 + 275.56 = √375.56 ≈ 19.39 cm
The area of the triangle = 0.5 * 19.39 * 16.6 ≈ 161.73 square cm
For the height of 17.2 cm:
Base of triangle = √(18/2)^2 + 17.2^2 = √81 +295.84 = √376.84 ≈ 19.4 cm
The area of the triangle = 0.5 * 19.4 * 17.2 ≈ 166.88 square cm
Since the pyramid has 4 triangular faces, the total surface area is the sum of the base area and the four triangular face areas:
360 (base) + 161.73 + 161.73 + 166.88 + 166.88 ≈ 1018.22 square cm
Therefore, the correct response is:
1,018.2 cm2