The object that has the attributes of a right rectangular prism is "b" (the book) and "c" (the house). However, since it seems you're looking for just one option, the best choice is "b" (the book), as it is more commonly recognized as a rectangular prism in everyday objects.
Use the image to answer the question.
(an image of a piece of pie labeled with "a.", a book labeled with "b", a house labeled with "c", and a shopping cart with 13 items labeled with "d")
which of these everyday objects has the attributes of a right rectangular prism?
b
d
c
a
9 answers
(an image of the pyramids of giza are shown)
Jamie has been assigned to replicate the pyramids of giza in egypt. what type of pyramids are these? Describe the attributes.
a. They are square pyramids. They have 4 faces. The 3 lateral faces are triangles, and the 4th face is a square base. Each pyramid has 6 vertices and 8 edges. The 3 lateral faces meet at a single point, or apex.
b.They are triangular pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
c. They are square pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
d. They are right rectangular pyramids. They have 6 faces. The 5 lateral faces are triangles, and the 6th face is a triangular base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
Jamie has been assigned to replicate the pyramids of giza in egypt. what type of pyramids are these? Describe the attributes.
a. They are square pyramids. They have 4 faces. The 3 lateral faces are triangles, and the 4th face is a square base. Each pyramid has 6 vertices and 8 edges. The 3 lateral faces meet at a single point, or apex.
b.They are triangular pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
c. They are square pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
d. They are right rectangular pyramids. They have 6 faces. The 5 lateral faces are triangles, and the 6th face is a triangular base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
The correct answer is c.
The attributes are:
- They are square pyramids.
- They have 5 faces: 4 triangular lateral faces and 1 square base.
- Each pyramid has 5 vertices and 8 edges.
- The 4 lateral faces meet at a single point, or apex.
This accurately describes the pyramids of Giza, which are indeed square pyramids.
an image of a rubix cube is shown
given that each square is 1 inch, find the surface area of this puzzle game.
54 cm^2
54 in.^2
18 in.^2
9 in.^2
given that each square is 1 inch, find the surface area of this puzzle game.
54 cm^2
54 in.^2
18 in.^2
9 in.^2
To find the surface area of a Rubik's Cube, we first note that it is a cube with each edge measuring 1 inch.
The formula for the surface area (SA) of a cube is:
\[ \text{SA} = 6a^2 \]
where \( a \) is the length of an edge.
In this case, since each edge is 1 inch:
\[ \text{SA} = 6(1^2) = 6 \text{ in}^2 \]
However, since a standard Rubik's Cube is typically made up of smaller squares and has a total of 54 smaller 1x1 squares (9 on each of its 6 faces), the total surface area is indeed \( 54 \text{ in}^2 \).
So, the correct answer is 54 in.^2.
Find the surface area of a rectangular pyramid with these measurements: l = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth.
___ m^2
___ m^2
To find the surface area of a rectangular pyramid, we need to consider both the base area and the area of the triangular lateral faces.
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Base Area: The base of the pyramid is a rectangle, and its area can be calculated using the formula: \[ \text{Base Area} = l \times w \] Given \( l = 15 , m \) and \( w = 12 , m \): \[ \text{Base Area} = 15 \times 12 = 180 , m^2 \]
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Lateral Surface Area: The lateral surface area consists of 4 triangular faces. To find the area of each triangular face, we need the slant height of the pyramid. We can find the slant height (\( s \)) using the Pythagorean theorem.
First, find the distance from the center of the base to a vertex (the apothem) using half of the width and length: \[ \text{Apothem} = \sqrt{\left( \frac{l}{2} \right)^2 + \left( \frac{h}{2} \right)^2} \] Substitute the values: \[ \text{half length} = \frac{l}{2} = \frac{15}{2} = 7.5 , m \] \[ \text{half width} = \frac{w}{2} = \frac{12}{2} = 6 , m \] The apothem to the center is simply: \[ \text{Apothem} = \sqrt{(7.5)^2 + (10)^2} = \sqrt{56.25 + 100} = \sqrt{156.25} = 12.5 , m \]
The area of one lateral triangular face is given by: \[ \text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} \] For each triangular face, the base will be the side length of the base (either length or width), and the height will be the slant height. We calculate the area for the two pairs of triangles:
- For the triangles on the length: \[ \text{Area} = \frac{1}{2} \times w \times s = \frac{1}{2} \times 12 \times 12.5 = 75 , m^2 \]
- For the triangles on the width: \[ \text{Area} = \frac{1}{2} \times l \times s = \frac{1}{2} \times 15 \times 12.5 = 93.75 , m^2 \]
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Total Lateral Surface Area: Since there are two triangles for each side: \[ \text{Total Lateral Area} = 2(\text{Area of length triangles}) + 2(\text{Area of width triangles}) = 2 \times 75 + 2 \times 93.75 = 150 + 187.5 = 337.5 , m^2 \]
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Total Surface Area: \[ \text{Total Surface Area} = \text{Base Area} + \text{Total Lateral Area} = 180 + 337.5 = 517.5 , m^2 \]
Therefore, the surface area of the rectangular pyramid is \( \boxed{517.50} , m^2 \).
use the image to answer the question.
An illustration shows a 3 D triangular prism. The side of the base is 4.5 centimeters. The perpendicular height of the triangular base is 3.9 centimeters. The perpendicular height of the lateral face from the apex to the center of the base is 3.5 centimeters. There are two right angle symbols to show the perpendicular lines. The heights are shown as dashed lines.
A metalworker is creating decorative points in the form of triangular pyramids to go on top of a fence she is building. She wants to know the surface area of each pyramid. Use the surface area formula to find the surface area of each pyramid based on the figure.
___ cm^2
An illustration shows a 3 D triangular prism. The side of the base is 4.5 centimeters. The perpendicular height of the triangular base is 3.9 centimeters. The perpendicular height of the lateral face from the apex to the center of the base is 3.5 centimeters. There are two right angle symbols to show the perpendicular lines. The heights are shown as dashed lines.
A metalworker is creating decorative points in the form of triangular pyramids to go on top of a fence she is building. She wants to know the surface area of each pyramid. Use the surface area formula to find the surface area of each pyramid based on the figure.
___ cm^2
To find the surface area of a triangular pyramid (tetrahedron), we will use the surface area formula for a triangular pyramid, which includes the area of the base and the areas of the triangular lateral faces.
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Calculate the Area of the Base: The base of the pyramid is a triangle. Given:
- Base side length \( b = 4.5 , \text{cm} \)
- Height \( h = 3.9 , \text{cm} \)
The area \( A \) of the triangular base is given by: \[ A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 4.5 \times 3.9 \]
Calculating the area: \[ A = \frac{1}{2} \times 4.5 \times 3.9 = \frac{1}{2} \times 17.55 = 8.775 , \text{cm}^2 \]
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Calculate the Area of the Lateral Faces: The pyramid has three triangular lateral faces. We need the lengths of the sides of the triangle which are the lateral edges (the edges connecting the apex of the pyramid to each vertex of the base).
Each lateral face is a triangle. We calculate the area of each face:
- The perpendicular height of the lateral triangular face (from the apex) is given as \( 3.5 , \text{cm} \).
- The base of each lateral face corresponds to one side of the triangular base. We need to find the lengths of the sides of the triangular base (in this case, since it's an isosceles triangle, we can assume two equal lengths and one base).
The lateral faces will share the same height \( 3.5 , \text{cm} \) from the apex to the midpoint of each side.
For simplicity, we assume the triangular base has two equal sides:
- Calculate the lengths of each lateral face (as they are not provided, we will assume for calculation purposes).
- If we consider the triangle to be isosceles with base \( 4.5 , \text{cm} \) and height \( 3.9 , \text{cm} \), the hypotenuse (lateral side) can be calculated:
To find the length \( s \) of one of the equal sides: \[ \text{Half base} = \frac{4.5}{2} = 2.25 , \text{cm} \] \[ s = \sqrt{(2.25)^2 + (3.9)^2} = \sqrt{5.0625 + 15.21} = \sqrt{20.2725} \approx 4.49 , \text{cm} \]
So, we have:
- The area of the lateral triangle with base \( 4.5 , \text{cm} \): \[ A_l = \frac{1}{2} \times b \times h = \frac{1}{2} \times 4.5 \times 3.5 \approx 7.875 , \text{cm}^2 \]
Area for three triangular lateral faces: \[ \text{Total Lateral Area} = 3 \times A_l = 3 \times 7.875 \approx 23.625 , \text{cm}^2 \]
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Total Surface Area: The total surface area \( SA \) of the pyramid is given by: \[ SA = \text{Base Area} + \text{Lateral Area} = 8.775 + 23.625 = 32.4 , \text{cm}^2 \]
Therefore, the surface area of each pyramid is approximately 32.40 cm².