After you break apart a rectangular pyramid, what two-dimensional shapes appear in the net?(1 point)
Responses
A). square and triangle
square and triangle
B). triangles
triangles
C). rectangles
rectangles
D). rectangle and triangles
rectangle and triangles
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters.
What is the total surface area of the figure?
(1 point)
____ mm2
The total surface area of the figure can be calculated by finding the surface area of each individual rectangular prism and then adding them together.
For the rectangular prism on the left:
Surface area = 2(length * width + width * height + length * height)
Surface area = 2(10*8 + 8*w + 10*w) -> 2(80 + 18w)
Surface area = 160 + 36w
For the rectangular prism on the right:
Surface area = 2(6*6 + 6*6 + 6*6)
Surface area = 2(36 + 36 + 36) -> 2(108)
Surface area = 216
Total surface area = Surface area of left prism + Surface area of right prism
Total surface area = 160 + 36w + 216
Total surface area = 376 + 36w
Therefore, the total surface area of the figure is 376 + 36w mm^2.
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a triangular prism stacked on top of a rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 32 meters, a width of 10 meters, and a height of 8 meters. The triangular prism has a rectangular base that is aligned on all edges with the rectangular prism below. The perpendicular height of the triangular prism is marked by a right angle symbol from the top vertex to the center of the triangular face. The height of the triangular face of the prism measures 12 meters. The sides of the triangular faces of the triangular prism measure 20 meters.
What is the total surface area of the figure?
(1 point)
m2
To find the total surface area of the figure, we need to calculate the surface area of each individual face of the figure and then add them together.
For the rectangular prism:
- Front and back faces: 32m * 8m = 256 m^2 (each)
- Top and bottom faces: 32m * 10m = 320 m^2 (each)
- Side faces: 10m * 8m = 80 m^2 (each)
Total surface area of the rectangular prism = 2(256) + 2(320) + 2(80) = 512 + 640 + 160 = 1312 m^2
For the triangular prism:
- Base of the triangle: 32m * 20m / 2 = 320 m^2
- Two triangular faces: 2(1/2 * 20m * 12m) = 240 m^2
Total surface area of the triangular prism = 320 + 240 = 560 m^2
Total surface area of the entire figure = Surface area of rectangular prism + Surface area of triangular prism
Total surface area = 1312 m^2 + 560 m^2 = 1872 m^2
Therefore, the total surface area of the figure is 1872 m^2.