Use the image to answer the question.
An illustration shows a net diagram of a triangular pyramid. The diagram shows a large triangle that is formed by 4 identical smaller triangles. An inverted triangle is the central figure inside the large triangle. Its sides are indicated by 3 dashed lines. The three vertices of the dashed line triangle touch the center of the three edges of the larger outer triangle. The 3 dashed line edges form the bases of the other 3 triangles. Each triangle represents a face of the tetrahedron. All 4 triangles have an area measuring 3 square meters.
Calculate the surface area of the triangular pyramid.
(1 point)
m2
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The surface area of a triangular pyramid is calculated by finding the area of each face, which in this case is 3 square meters for each triangular face, and then adding them all together.
Since there are 4 identical triangular faces, the total surface area of the triangular pyramid would be:
4 x 3 = 12 square meters
Therefore, the surface area of the triangular pyramid is 12 square meters.
Use the image to answer the question.
An illustration shows a 3 D triangular pyramid. The edges that are not visible are represented by dashed lines. The pyramid base is an equilateral triangle with sides measuring 4 centimeters and a perpendicular height of 3.46 centimeters. The side faces of the pyramid are isosceles triangles with sides of 6.32 centimeters, a base of 4 centimeters, and a slant height of 6 centimeters, represented by a dashed line from the apex to the center of a base edge.
Complete the net of the pyramid. Enter the length of each section on the net.
(2 points)
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To complete the net of the pyramid, we first determine the lengths of each section based on the given information about the pyramid's dimensions.
1. The base of the pyramid is an equilateral triangle with sides measuring 4 cm each. Therefore, each side of the equilateral triangle on the net would be 4 cm.
2. For the side faces of the pyramid, which are isosceles triangles with sides of 6.32 cm, a base of 4 cm, and a slant height of 6 cm, we need to construct two triangles on the net. Each of these triangles should have the following lengths:
- The two equal sides of the isosceles triangle are 6.32 cm each.
- The base of the isosceles triangle is 4 cm.
- The slant height (height from the apex to the center of the base edge) is 6 cm.
Therefore, the lengths of each section on the net would be:
- Equilateral triangle sides: 4 cm
- Isosceles triangle sides: 6.32 cm
- Isosceles triangle base: 4 cm
- Isosceles triangle slant height: 6 cm
These lengths would allow you to accurately complete the net of the triangular pyramid.
there are not two 4s
To accurately complete the net of the triangular pyramid, we need to consider the dimensions provided.
1. The base of the pyramid is an equilateral triangle with sides measuring 4 cm each. Therefore, each side length of the equilateral triangle on the net would be 4 cm.
2. For the side faces of the pyramid, which are isosceles triangles with sides of 6.32 cm, a base of 4 cm, and a slant height of 6 cm, we need to construct two triangles on the net. Each of these triangles should have the following lengths:
- The two equal sides of the isosceles triangle are 6.32 cm each.
- The base of the isosceles triangle is 4 cm.
- The slant height (height from the apex to the center of the base edge) is 6 cm.
Therefore, the lengths of each section on the net would be:
- Equilateral triangle sides: 4 cm
- Isosceles triangle side lengths: 6.32 cm
- Isosceles triangle base: 4 cm
- Isosceles triangle slant height: 6 cm
Using these measurements, you can accurately complete the net of the triangular pyramid.
After learning about the Egyptians, Mr. Pink’s class wants to create their own pyramids with triangular bases. Each group needs to create their measurements and identify how much butcher paper they will need to construct their pyramid before they can start. Riley’s group has determined that they want to have an equilateral triangle base of 12 inches and a height of 10.4 inches. The three sides will be isosceles triangles measuring 10 inches by 10 inches by 12 inches with an 8-inch height. How much total paper will Riley’s group need to construct their pyramid? Write your answer in decimal form.(1 point)
in.2
To calculate the total amount of paper that Riley's group will need to construct their pyramid, we need to determine the total surface area of the pyramid.
1. The base of the pyramid is an equilateral triangle with a side length of 12 inches and a height of 10.4 inches. The area of an equilateral triangle can be calculated using the formula A = sqrt(3)/4 * side length^2. Plugging in the values, we have A = sqrt(3)/4 * 12^2 = 36*sqrt(3) square inches.
2. The three side faces are isosceles triangles with base sides of 10 inches and 12 inches (hypotenuse), and a height of 8 inches. The area of an isosceles triangle can be calculated as A = 1/2 * base * height. Each triangle will have an area of 1/2 * 10 * 8 = 40 square inches plus 1/2 * 12 * 8 = 48 square inches. Since there are three identical triangles, the total area of the side faces would be 3 * (40 + 48) = 264 square inches.
Now, calculate the total paper needed by adding the areas of the base and side faces:
Total paper needed = Area of base + Area of side faces
Total paper needed = 36*sqrt(3) + 264 square inches
Total paper needed ≈ 461.65 square inches
Therefore, Riley's group will need approximately 461.65 square inches of butcher paper to construct their pyramid.