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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
= \sqrt{\left(\frac{w}{2}\right)^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 sum of the areas of the base and the four triangular faces.
Given that the base is a square with a side of 15 feet, the area of the base is:
Area of base = side^2 = 15^2 = 225 square feet
The lateral faces of the pyramid are triangles. To find the area of one triangular face, we need to find the base of the triangle which is the side of the square (15 feet) and the height of the triangular face. The height of the triangular face is the slant height of the pyramid which can be found using Pythagoras theorem:
h = √(15/2)^2 + 9.9^2 = √(7.5)^2 + 9.9^2 = √(56.25 + 98.01) = √154.26 ≈ 12.42 feet
Area of one triangular face = (1/2) * base * height = (1/2) * 15 * 12.42 ≈ 93.15 square feet
Since there are four triangular faces, the total area of the four lateral faces = 4 * 93.15 = 372.6 square feet
Therefore, the total surface area of the square pyramid is:
Total surface area = base area + lateral face areas = 225 + 372.6 ≈ 597.6 square feet
So, the closest option 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 or square pyramid, we need to calculate the sum of the areas of the base and the four triangular faces.
Given that the base is a rectangle with a length of 20 cm and a width of 18 cm, the area of the base is:
Area of base = length * width = 20 * 18 = 360 square centimeters.
The lateral faces of the pyramid are triangles. To find the area of one triangular face, we need to find the base of the triangle, which is either the length or the width of the base, and the height of the triangular face. We have two different heights given:
- Height for the face with base length of 20 cm = 16.6 cm
- Height for the face with base length of 18 cm = 17.2 cm
Area of one triangular face with base length of 20 cm = (1/2) * base * height = (1/2) * 20 * 16.6 = 166 square centimeters.
Area of one triangular face with base length of 18 cm = (1/2) * base * height = (1/2) * 18 * 17.2 = 154.8 square centimeters.
Since there are two triangular faces with different areas, we calculate the total area contributed by the lateral faces:
Total lateral face area = 166 + 154.8 = 320.8 square centimeters.
Therefore, the total surface area of the rectangular pyramid is:
Total surface area = base area + lateral face areas = 360 + 320.8 = 680.8 square centimeters.
So, the closest option is 1,001.6 cm².