Use the image to answer the question.
An illustration shows a pyramid with a square base. The side of the base is labeled 15 feet. The perpendicular height denoted by a right angle symbol on the lateral face from the apex to the base is labeled 9.9 feet.
Solve for the surface area of the square pyramid.
(1 point)
Responses
522 ft.2
522 ft. squared
819 ft.2
819 ft. squared
299.25 ft.2
299.25 ft. squared
148.5 ft.2
The Answers to Unit 2 Lesson 7 Surface Area of Rectangular Pyramids Quick Check
Q1:After you break apart a rectangular pyramid, what two-dimensional shapes appear in the net?
A: Rectangles and triangles
Q2:What is the formula to solve for the slant height of the side triangles in the rectangular pyramid?
A:=√(l/2) square + h square
Q3:Solve for the surface area of the square pyramid.
A: 522 ft 2 (square)
Q4:What is the slant height in a rectangular or square pyramid?
A:the height from the apex straight down to the base of the triangular face where it forms a right angle
Q5:What is the surface of the rectangular pyramid?
A: 1,001.6 cm 2 (square)
The surface area of a square pyramid can be calculated using the formula:
Surface Area = base area + (1/2) * perimeter of base * slant height
First, calculate the base area:
Base area = 15 ft * 15 ft = 225 ft^2
Next, calculate the slant height of the pyramid using the Pythagorean theorem:
Slant height = sqrt(9.9 ft^2 + (15/2)^2)
Slant height = sqrt(9.9 ft^2 + 112.5 ft^2)
Slant height = sqrt(122.4 ft^2)
Slant height ≈ 11.06 ft
Now, calculate the perimeter of the base:
Perimeter of the base = 4 * 15 ft = 60 ft
Finally, calculate the surface area of the pyramid:
Surface Area = 225 ft^2 + (1/2) * 60 ft * 11.06 ft
Surface Area = 225 ft^2 + 330.9 ft^2
Surface Area ≈ 555.9 ft^2
So the surface area of the square pyramid is approximately 555.9 ft^2. Since this is not one of the provided answer options, it seems like the closest option is 522 ft^2 or 522 ft. squared.
which one is it
522 ft. squared
819 ft. squared
299.25 ft. squared
148.5 ft. squared
The correct answer is:
522 ft. squared
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 20 centimeters and the width as 18 centimeters. The perpendicular heights from the apex to the base length of 20 is 16.6 centimeters and to the base width of 18 is 17.2 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 of the rectangular pyramid?
(1 point)
Responses
1,178.8 cm2
1,178.8 cm squared
102,787.2 cm2
102,787.2 cm squared
1,001.6 cm2
1,001.6 cm squared
1,643.2 cm2
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = base area + (1/2) * perimeter of base * slant height
First, calculate the base area:
Base area = length * width = 20 cm * 18 cm = 360 cm^2
Next, calculate the slant height for each rectangle:
For the height of 20 cm:
Slant height = sqrt(16.6 cm^2 + (20/2)^2)
Slant height = sqrt(16.6 cm^2 + 100 cm^2)
Slant height = sqrt(116.6 cm^2)
Slant height ≈ 10.8 cm
For the height of 18 cm:
Slant height = sqrt(17.2 cm^2 + (18/2)^2)
Slant height = sqrt(17.2 cm^2 + 81 cm^2)
Slant height = sqrt(98.2 cm^2)
Slant height ≈ 9.9 cm
Now, calculate the perimeter of the base:
Perimeter of the base = 2*(length + width) = 2*(20 cm + 18 cm) = 76 cm
Finally, calculate the surface area of the pyramid:
Surface Area = 360 cm^2 + (1/2) * 76 cm * (10.8 cm + 9.9 cm)
Surface Area = 360 cm^2 + 38 cm * 20.7 cm
Surface Area = 360 cm^2 + 785.4 cm^2
Surface Area = 1145.4 cm^2
So, the surface area of the rectangular pyramid is approximately 1145.4 cm^2, which is closest to the first provided option:
1,178.8 cm squared.