Question 1
A)
Use the image to answer the question.
An illustration shows a triangular pyramid. The perpendicular height of the base measures 3.9 centimeters and its sides measure 4.5 centimeters. The slant height measures 3.5 centimeters.
Find the surface area of the solid figure with an equilateral triangle base.
(1 point)
$$ cm2
Question 2
A)
Use the image to answer the question.
An illustration shows the net of a triangular prism. The illustration forms a shape where the small triangle is in the middle with each side being the base of three different triangles. The height of the triangle in the middle is 14.0 meters and the base is 16.2 meters. The height of the triangles at the side is 14.5 meters. There is a right angle symbol in the middle triangle and the triangle to the right.
Find the surface area of the net given an equilateral triangle as the base.
(1 point)
$$ m2
Question 3
A)
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)
$$ m2
Question 4
A)
Use the image to answer the question.
An illustration shows a 3 D triangular pyramid. The edges that are not visible are represented by dashed lines. The pyramid base is an equilateral triangle with sides measuring 4 centimeters and a perpendicular height of 3.46 centimeters. The side faces of the pyramid are isosceles triangles with sides of 6.32 centimeters, a base of 4 centimeters, and a slant height of 6 centimeters, represented by a dashed line from the apex to the center of a base edge.
Complete the net of the pyramid. Enter the length of each section on the net.
(2 points)
$$
$$
$$
$$
Question 5
A)After learning about the Egyptians, Mr. Pink’s class wants to create their own pyramids with triangular bases. Each group needs to create their measurements and identify how much butcher paper they will need to construct their pyramid before they can start. Riley’s group has determined that they want to have an equilateral triangle base of 12 inches and a height of 10.4 inches. The three sides will be isosceles triangles measuring 10 inches by 10 inches by 12 inches with an 8-inch height. How much total paper will Riley’s group need to construct their pyramid? Write your answer in decimal form.(1 point)
$$ in.2
Question 1
Surface area = Area of base + Area of three lateral faces
Area of equilateral triangle base = (sqrt(3)/4) * side^2
Area of base = (sqrt(3)/4) * 4.5^2 = 5.51925 cm^2
Area of each lateral face = (1/2) * base * slant height
Area of each lateral face = (1/2) * 4.5 * 3.5 = 7.875 cm^2
Total surface area = 5.51925 + 3(7.875) = 29.14425 cm^2
So, the surface area of the triangular pyramid is 29.14425 cm^2.
Question 2
Surface area = Area of two triangular bases + Area of three rectangular faces
Area of equilateral triangle base = (sqrt(3)/4) * side^2
Area of triangular base = (sqrt(3)/4) * 16.2^2 = 44.0787 m^2
Area of each rectangular face = base * height
Area of each rectangular face = 16.2 * 14 = 226.8 m^2
Total surface area = 2(44.0787) + 3(226.8) = 768.557 m^2
So, the surface area of the triangular prism is 768.557 m^2.
Question 3
Surface area of a triangular pyramid = Area of base + Sum of areas of three triangular faces
Given that each triangular face has an area of 3 square meters:
Total surface area = 3 + 3(3) = 12 square meters
So, the surface area of the triangular pyramid is 12 square meters.
Question 4
The net of the triangular pyramid consists of:
- 1 equilateral triangle for the base
- 3 isosceles triangles for the side faces
The side faces will have different dimensions. The dimensions provided in the question don't specify which side face corresponds to which measurement, so we can't determine the exact lengths of each section on the net without additional information.
Question 5
Total paper needed = Area of equilateral triangle base + 3 times Area of isosceles triangle side
Area of equilateral triangle base = (sqrt(3)/4) * 12^2 = 31.176 m^2
Area of each isosceles triangle side = (1/2) * base * height = (1/2) * 10 * 8 = 40 in^2
Total paper needed = 31.176 + 3(40) = 151.176 in^2
So, Riley's group will need a total of 151.176 square inches of paper to construct their pyramid.
wrong
I apologize for the mistake. Let me correct the calculations:
Question 1:
Surface area = Area of base + Area of three lateral faces
Area of equilateral triangle base = (sqrt(3)/4) * side^2
Area of triangular base = (sqrt(3)/4) * 4.5^2 = 5.1935 cm^2
Area of each lateral face = (1/2) * base * slant height
Area of each lateral face = (1/2) * 4.5 * 3.5 = 7.875 cm^2
Total surface area = 5.1935 + 3(7.875) = 28.8195 cm^2
So, the surface area of the triangular pyramid is 28.8195 cm^2.
Question 2:
Surface area = Area of two triangular bases + Area of three rectangular faces
Area of equilateral triangle base = (sqrt(3)/4) * side^2
Area of triangular base = (sqrt(3)/4) * 16.2^2 = 44.2716 m^2
Area of each rectangular face = base * height
Area of each rectangular face = 16.2 * 14 = 226.8 m^2
Total surface area = 2(44.2716) + 3(226.8) = 750.0132 m^2
So, the surface area of the triangular prism is 750.0132 m^2.
Question 3:
Surface area of a triangular pyramid = Area of base + Sum of areas of three triangular faces
Given that each triangular face has an area of 3 square meters:
Total surface area = 3 + 3(3) = 12 square meters
So, the surface area of the triangular pyramid is 12 square meters.
Question 4:
Without additional information, it's not possible to determine the exact lengths of each section on the net.
Question 5:
Total paper needed = Area of equilateral triangle base + 3 times Area of isosceles triangle side
Area of equilateral triangle base = (sqrt(3)/4) * 12^2 = 31.176 m^2
Area of each isosceles triangle side = (1/2) * base * height = (1/2) * 10 * 8 = 40 in^2
Total paper needed = 31.176 + 3(40) = 151.176 in^2
So, Riley's group will need a total of 151.176 square inches of paper to construct their pyramid.
wrong the hell fix it
My apologies for the errors in the previous responses. Let's correct the calculations:
Question 1:
Surface area = Area of base + Area of three lateral faces
Area of equilateral triangle base = (sqrt(3)/4) * side^2
Area of triangular base = (sqrt(3)/4) * 4.5^2 = 5.888 cm^2
Area of each lateral face = (1/2) * base * slant height
Area of each lateral face = (1/2) * 4.5 * 3.5 = 7.875 cm^2
Total surface area = 5.888 + 3(7.875) = 29.513 cm^2
So, the surface area of the triangular pyramid is 29.513 cm^2.
Question 2:
Surface area = Area of two triangular bases + Area of three rectangular faces
Area of equilateral triangle base = (sqrt(3)/4) * side^2
Area of triangular base = (sqrt(3)/4) * 16.2^2 = 46.733 m^2
Area of each rectangular face = base * height
Area of each rectangular face = 16.2 * 14 = 226.8 m^2
Total surface area = 2(46.733) + 3(226.8) = 723.366 m^2
So, the surface area of the triangular prism is 723.366 m^2.
Question 3:
Total surface area of the triangular pyramid is the sum of the areas of all its faces:
Each triangular face is 3 square meters, so the total surface area is 3 * 4 = 12 square meters.
So, the surface area of the triangular pyramid is 12 square meters.
If you have any further questions, feel free to ask.