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A rectangular pyramid is labeled with the following dimensions. The front left edge of the rectangular base is labeled 6. The front right edge of the rectangular base is labeled 4. There is a dashed line labeled 4 that extends from the apex to the middle of the line labeled 6. There is another dashed line labeled 4 point 6 that extends from the apex to the middle of the line labeled 4.
The rectangular pyramid could be decomposed into which of the following nets?
(1 point)
7 answers
The rectangular pyramid could be decomposed into a net that consists of a rectangle and two triangles.
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An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 centimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
What is the surface area of the rectangular pyramid?
(1 point)
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 centimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
What is the surface area of the rectangular pyramid?
(1 point)
To calculate the surface area of the rectangular pyramid, we need to find the areas of each of the faces and then add them together.
1. The area of the rectangular base is given by: Area = length x width = 14 cm x 12 cm = 168 square cm.
2. The area of each of the triangular faces can be calculated using the formula for the area of a triangle: Area = 1/2 * base * height.
a. For the face with base 14 cm and height 10 cm, the area is: 1/2 * 14 cm * 10 cm = 70 square cm.
b. For the face with base 12 cm and height 10.6 cm, the area is: 1/2 * 12 cm * 10.6 cm = 63.6 square cm.
Now, you can find the total surface area by summing the areas of the base and the two triangular faces:
Total surface area = Area of base + 2 * Area of triangular faces
Total surface area = 168 cm^2 + 70 cm^2 + 63.6 cm^2
Total surface area = 301.6 square cm
Therefore, the surface area of the rectangular pyramid is 301.6 square centimeters.
1. The area of the rectangular base is given by: Area = length x width = 14 cm x 12 cm = 168 square cm.
2. The area of each of the triangular faces can be calculated using the formula for the area of a triangle: Area = 1/2 * base * height.
a. For the face with base 14 cm and height 10 cm, the area is: 1/2 * 14 cm * 10 cm = 70 square cm.
b. For the face with base 12 cm and height 10.6 cm, the area is: 1/2 * 12 cm * 10.6 cm = 63.6 square cm.
Now, you can find the total surface area by summing the areas of the base and the two triangular faces:
Total surface area = Area of base + 2 * Area of triangular faces
Total surface area = 168 cm^2 + 70 cm^2 + 63.6 cm^2
Total surface area = 301.6 square cm
Therefore, the surface area of the rectangular pyramid is 301.6 square centimeters.
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An illustration shows a three dimensional composite figure formed by a right triangular prism placed 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 12 feet and a height of 8 feet. The width of the rectangular prism is 8 feet. The edges of the hidden side face of the right triangular prism align perfectly with the edges of the hidden top face of the rectangular prism. The right triangular prism is aligned to the left of the rectangular prism. The height of the right triangular prism is not shown. The total height of the left side of the figure is 20 feet. The right triangular prism has a width of 8 feet. The hypotenuse side of the right triangular prism has a length of 15 feet.
What is the surface area of the figure?
(1 point)
_ft.2
An illustration shows a three dimensional composite figure formed by a right triangular prism placed 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 12 feet and a height of 8 feet. The width of the rectangular prism is 8 feet. The edges of the hidden side face of the right triangular prism align perfectly with the edges of the hidden top face of the rectangular prism. The right triangular prism is aligned to the left of the rectangular prism. The height of the right triangular prism is not shown. The total height of the left side of the figure is 20 feet. The right triangular prism has a width of 8 feet. The hypotenuse side of the right triangular prism has a length of 15 feet.
What is the surface area of the figure?
(1 point)
_ft.2
To calculate the surface area of the composite figure formed by placing a right triangular prism on top of a rectangular prism, we need to find the sum of the surface areas of each individual shape.
1. Surface area of the rectangular prism:
There are three pairs of rectangular faces on a rectangular prism. Two pairs have dimensions 12 feet by 8 feet, and one pair has dimensions 8 feet by 8 feet.
Total surface area of the rectangular prism = 2*(12*8 + 8*8) = 2*(96 + 64) = 2*(160) = 320 square feet.
2. Surface area of the right triangular prism:
The right triangular prism has one triangular face and three rectangular faces.
The triangular face has dimensions of base = 12 feet, height = 8 feet, and hypotenuse = 15 feet.
Using the formula for the area of a triangle: area = 0.5 * base * height = 0.5 * 12 * 8 = 48 square feet.
Each rectangular face has a base of 12 feet and a height that is the height of the prism (unknown).
The height of the right triangular prism can be calculated using the total height of the figure and the known height of the rectangular prism:
Total height of the figure = height of rectangular prism + height of right triangular prism
20 feet = 8 feet + height of right triangular prism
height of right triangular prism = 12 feet
The surface area of three identical rectangular faces is: 3 * (12 * 12) = 432 square feet.
Finally, calculate the total surface area of the composite figure by summing the surface areas of the rectangular prism and the right triangular prism:
Total surface area = Surface area of rectangular prism + Surface area of right triangular prism = 320 + 48 + 432 = 800 square feet.
Therefore, the surface area of the composite figure is 800 square feet.
1. Surface area of the rectangular prism:
There are three pairs of rectangular faces on a rectangular prism. Two pairs have dimensions 12 feet by 8 feet, and one pair has dimensions 8 feet by 8 feet.
Total surface area of the rectangular prism = 2*(12*8 + 8*8) = 2*(96 + 64) = 2*(160) = 320 square feet.
2. Surface area of the right triangular prism:
The right triangular prism has one triangular face and three rectangular faces.
The triangular face has dimensions of base = 12 feet, height = 8 feet, and hypotenuse = 15 feet.
Using the formula for the area of a triangle: area = 0.5 * base * height = 0.5 * 12 * 8 = 48 square feet.
Each rectangular face has a base of 12 feet and a height that is the height of the prism (unknown).
The height of the right triangular prism can be calculated using the total height of the figure and the known height of the rectangular prism:
Total height of the figure = height of rectangular prism + height of right triangular prism
20 feet = 8 feet + height of right triangular prism
height of right triangular prism = 12 feet
The surface area of three identical rectangular faces is: 3 * (12 * 12) = 432 square feet.
Finally, calculate the total surface area of the composite figure by summing the surface areas of the rectangular prism and the right triangular prism:
Total surface area = Surface area of rectangular prism + Surface area of right triangular prism = 320 + 48 + 432 = 800 square feet.
Therefore, the surface area of the composite figure is 800 square feet.
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An illustration shows a 3-dimensional vertical rectangular prism that appears as the letter upper C, with a rectangular portion removed from the right center. The rectangular prism is 15 feet high, 10 feet wide, and 1 foot deep. The width of the portion removed from the middle on the right side is 7 feet across. The height of the remaining two arms left at the top and bottom is 4 feet each.
In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C . What is its surface area?
(1 point)
how many ft.2
An illustration shows a 3-dimensional vertical rectangular prism that appears as the letter upper C, with a rectangular portion removed from the right center. The rectangular prism is 15 feet high, 10 feet wide, and 1 foot deep. The width of the portion removed from the middle on the right side is 7 feet across. The height of the remaining two arms left at the top and bottom is 4 feet each.
In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C . What is its surface area?
(1 point)
how many ft.2
To calculate the surface area of the 3-dimensional vertical rectangular prism in the shape of the letter "C", we need to find the surface areas of each face of the prism.
1. Front Face:
The front face of the rectangular prism is a rectangle with dimensions 10 feet by 15 feet.
Area = length x width = 10 ft x 15 ft = 150 square feet.
2. Top and Bottom Faces:
Each of the top and bottom faces of the rectangular prism is a rectangle with dimensions 7 feet by 15 feet (as the central 7 feet width part is removed). There are two such faces.
Area of each face = length x width = 7 ft x 15 ft = 105 square feet.
Total area of top and bottom faces = 2 x 105 = 210 square feet.
3. Remaining Two Arms:
The two remaining arms of the "C" shape have dimensions of 4 feet in height, 1 foot in depth, and the width of 7 feet.
Each arm forms a rectangular face with dimensions 4 feet by 7 feet.
Area of each arm = length x width = 4 ft x 7 ft = 28 square feet.
Total area of the two arms = 2 x 28 = 56 square feet.
Now, we sum the areas of all the faces to get the total surface area of the "C" shaped rectangular prism:
Total Surface Area = Front Face + Top and Bottom Faces + Remaining Arms
Total Surface Area = 150 ft^2 + 210 ft^2 + 56 ft^2 = 416 square feet.
Therefore, the surface area of the vertical rectangular prism shaped like the letter "C" is 416 square feet.
1. Front Face:
The front face of the rectangular prism is a rectangle with dimensions 10 feet by 15 feet.
Area = length x width = 10 ft x 15 ft = 150 square feet.
2. Top and Bottom Faces:
Each of the top and bottom faces of the rectangular prism is a rectangle with dimensions 7 feet by 15 feet (as the central 7 feet width part is removed). There are two such faces.
Area of each face = length x width = 7 ft x 15 ft = 105 square feet.
Total area of top and bottom faces = 2 x 105 = 210 square feet.
3. Remaining Two Arms:
The two remaining arms of the "C" shape have dimensions of 4 feet in height, 1 foot in depth, and the width of 7 feet.
Each arm forms a rectangular face with dimensions 4 feet by 7 feet.
Area of each arm = length x width = 4 ft x 7 ft = 28 square feet.
Total area of the two arms = 2 x 28 = 56 square feet.
Now, we sum the areas of all the faces to get the total surface area of the "C" shaped rectangular prism:
Total Surface Area = Front Face + Top and Bottom Faces + Remaining Arms
Total Surface Area = 150 ft^2 + 210 ft^2 + 56 ft^2 = 416 square feet.
Therefore, the surface area of the vertical rectangular prism shaped like the letter "C" is 416 square feet.
1 answer