After you break apart a rectangular pyramid, what two-dimensional shapes appear in the net?(1 point)
rectangles
triangles
rectangle and triangles
square and triangle
rectangle and triangles
What is the formula to solve for the slant height of the side triangles in the rectangular pyramid?
The formula to solve for the slant height of the side triangles in a rectangular pyramid is:
\[ \text{Slant height} = \sqrt{h^2 + (\frac{l}{2})^2} \]
Where:
- \( h \) is the height of the rectangular pyramid
- \( l \) is the length of the base of the triangle
15 ft. long 9.9 ft. tall
Solve for the surface area of the square pyramid.
(1 point)
299.25 ft.2
2
522 ft.2
2
819 ft.2
2
148.5 ft.2
To solve for the surface area of a square pyramid, we need to find the areas of the square base and the four triangular faces.
Given:
Length of base = 15 ft.
Height = 9.9 ft.
1. The area of the square base:
Area = side^2
Area = 15^2
Area = 225 ft^2
2. The area of the four triangular faces:
We need to find the slant height first using the formula mentioned earlier:
Slant height = √(height^2 + (side/2)^2)
Slant height = √(9.9^2 + (15/2)^2)
Slant height = √(98.01 + 56.25)
Slant height = √154.26
Slant height ≈ 12.42 ft.
Now the area of one triangular face:
Area = 1/2 * base * height
Area = 1/2 * 15 * 12.42
Area ≈ 93.15 ft^2
Total area of all four triangular faces:
4 * (93.15) ≈ 372.6 ft^2
3. Total surface area:
Surface area = Area of base + Total area of all triangular faces
Surface area = 225 + 372.6
Surface area ≈ 597.6 ft^2
Therefore, the surface area of the square pyramid is approximately 597.6 ft^2.
What is the slant height in a rectangular or square pyramid?(1 point)
an edge of a triangular face
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 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
16.6 tall face 20 wide face 18 long face 17.2 tall side face
What is the surface of the rectangular pyramid?
(1 point)
1, 178.8 cm2
1, 001.6 cm2
1, 643.2 cm2
To find the surface area of the rectangular pyramid, we need to calculate the area of each face and add them together.
Given dimensions:
- Tall face: Height = 16.6 cm and Width = 20 cm
- Wide Face: Width = 20 cm and Length = 18 cm
- Long Face: Length = 18 cm and Height = 16.6 cm
- Tall Side Face: Slant Height = 17.2 cm
1. Area of Tall Face:
Area = Height * Width
Area = 16.6 cm * 20 cm
Area = 332 cm^2
2. Area of Wide Face:
Area = Width * Length
Area = 20 cm * 18 cm
Area = 360 cm^2
3. Area of Long Face:
Area = Length * Height
Area = 18 cm * 16.6 cm
Area = 298.8 cm^2
4. Area of Side Face (Triangular face):
Area = 1/2 * Base * Height
Area = 1/2 * 18 cm * 17.2 cm
Area = 155.4 cm^2
Now, calculate the total surface area by adding all the areas:
Total Surface Area = Tall Face + Wide Face + Long Face + Side Face
Total Surface Area = 332 cm^2 + 360 cm^2 + 298.8 cm^2 + 155.4 cm^2
Total Surface Area = 1146.2 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 1,146.2 cm^2.
The closest option provided is 1,178.8 cm^2, so the correct answer is 1,178.8 cm^2.