Use the image to answer the question.
An illustration shows a slide slice where a triangular plane with a square frame is inserted into a 3 D pyramid through one of the edges. The plane is positioned till the apex is reached and the middle triangular portion of the pyramid is highlighted.
What two-dimensional shape is created by slicing a right rectangular pyramid perpendicular to the base?
(1 point)
The two-dimensional shape created by slicing a right rectangular pyramid perpendicular to the base is a triangle.
Surface Area Unit Test
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Question
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base of length 6 meters and width 2 meters. The perpendicular height from the apex to the center of the base is labeled 8.8 meters. The slant height from the apex to the center of the width of the rectangle is labeled 9 meters. Both heights are drawn as dotted lines. The sides that are not visible are shown in dashed lines.
When finding the surface area of the rectangular pyramid, what dimension will be used to find the height of the triangular sides?(1 point)
The slant height (9 meters) will be used to find the height of the triangular sides when finding the surface area of the rectangular pyramid.
Use the image to answer the question.
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 find the surface area of a rectangular pyramid, we need to calculate the area of the base and the lateral faces.
1. Area of the base:
The area of a rectangle is given by length x width. In this case, the base of the pyramid is a rectangle with a length of 14 cm and a width of 12 cm.
Area of base = 14 cm x 12 cm = 168 square cm
2. Area of the lateral faces:
The lateral faces of the pyramid are triangles. To find the area of each triangle, we can use the formula: 1/2 x base x height, where the base is the length of the side of the rectangle and the height is the perpendicular height from the apex to the base.
a) For the side with a length of 14 cm:
Area = 1/2 x 14 cm x 10 cm = 70 square cm
b) For the side with a length of 12 cm:
Area = 1/2 x 12 cm x 10.6 cm = 63.6 square cm
3. Total surface area:
Add the area of the base and the two lateral faces.
Total surface area = Area of base + 2 x Area of lateral faces
Total surface area = 168 + 70 + 63.6 = 301.6 square cm
Therefore, the surface area of the rectangular pyramid is 301.6 square cm.
Use the image to answer the question.
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)
To find the surface area of the composite figure, we need to calculate the surface areas of each individual prism and then sum them up.
1. Surface Area of the Rectangular Prism:
A rectangular prism has 6 faces - 2 rectangles for the top and bottom, and 4 rectangles for the sides.
Given:
Length = 12 feet
Width = 8 feet
Height = 8 feet
Surface Area of the Rectangular Prism (A_rect) = 2lw + 2lh + 2wh
A_rect = 2(12)(8) + 2(12)(8) + 2(8)(8)
A_rect = 192 + 192 + 128
A_rect = 512 square feet
2. Surface Area of the Right Triangular Prism:
The right triangular prism has 5 faces - 2 triangular ends and 3 rectangular sides.
Given:
Width = 8 feet
Hypotenuse side = 15 feet
Height (not given, but needed for surface area calculation)
To find the height of the right triangular prism, we can use the Pythagorean theorem:
a^2 + b^2 = c^2, where a and b are the two legs of the right triangle and c is the hypotenuse.
Using c = 15 and one leg as 8 (the width), we find the other leg:
8^2 + b^2 = 15^2
64 + b^2 = 225
b^2 = 225 - 64
b = √161 ≈ 12.69 feet (approx.)
The height of the right triangular prism is approximately 12.69 feet.
Surface Area of the Right Triangular Prism (A_tri) = Area of the two triangles + Area of the three rectangular sides
A_tri = 2(1/2 * base * height) + 3(l*w)
A_tri = 2(1/2 * 8 * 12.69) + 3(15 * 8)
A_tri = 2(50.76) + 360
A_tri = 101.52 + 360
A_tri = 461.52 square feet
3. Total Surface Area of the Composite Figure:
Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Right Triangular Prism
Total Surface Area = 512 + 461.52
Total Surface Area = 973.52 square feet
Therefore, the surface area of the composite figure is approximately 973.52 square feet.
Use the image to answer the question.
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?
To find the surface area of the letter "C" depicted in the illustration, we need to calculate the surface area of each component separately and then sum them up.
1. Surface Area of the Front and Back Rectangular Faces (Top and Bottom Arm of the "C"):
The front and back faces of the rectangular prism that form the top and bottom arm of the "C" are rectangles.
Given:
Width = 10 feet
Height = 4 feet
Depth = 1 foot (for both arms)
Surface Area of a Rectangle (Front and Back Faces) = 2lw
S_A1 = 2(10)(4)
S_A1 = 80 square feet
2. Surface Area of the Remaining Center Part (Middle Section of the "C"):
The remaining portion has a width of 7 feet, a height of 15 feet (total height of the prism), and a depth of 1 foot (same as the arms).
Surface Area of a Rectangle = lw
S_A2 = 7 * 15
S_A2 = 105 square feet
3. Surface Area of the Side Faces (Two Vertical Sides of the "C"):
The side faces are rectangles with dimensions:
Height = 15 feet
Depth = 1 foot
Surface Area of a Rectangle = lh
S_A3 = 15 * 1
S_A3 = 15 square feet (per side, and there are 2 sides)
4. Total Surface Area:
To find the total surface area, sum up the areas of all the components.
Total Surface Area = 2(Front and Back Faces) + Middle Section + 2(Side Faces)
Total Surface Area = 2(80) + 105 + 2(15)
Total Surface Area = 160 + 105 + 30
Total Surface Area = 295 square feet
Therefore, the surface area of the letter "C" sculpture is 295 square feet.