Surface Area of Rectangular Pyramids Quick Check
3 of 53 of 5 Items
Question
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 surface area of a square pyramid can be calculated using the formula:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, find the Base Area:
Base Area = side^2
Base Area = 15^2
Base Area = 225 ft^2
Next, find the Perimeter of the Base:
Perimeter of Base = 4 * side
Perimeter of Base = 4 * 15
Perimeter of Base = 60 ft
Now, find the Slant Height (which is the height of one of the triangular faces):
Slant Height = sqrt((1/2 * side)^2 + height^2)
Slant Height = sqrt((1/2 * 15)^2 + 9.9^2)
Slant Height = sqrt(112.5 + 98.01)
Slant Height = sqrt(210.51)
Slant Height = 14.5 ft (approximately)
Finally, calculate the Surface Area:
Surface Area = 225 + (1/2) * 60 * 14.5
Surface Area = 225 + 435
Surface Area = 660 ft^2
So, the correct answer is:
819 ft.2
are you positve
My apologies for the error in my previous response. Let's recalculate.
Using the formula for the surface area of a square pyramid:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, find the Base Area:
Base Area = side^2
Base Area = 15^2
Base Area = 225 ft^2
Next, find the Perimeter of the Base:
Perimeter of Base = 4 * side
Perimeter of Base = 4 * 15
Perimeter of Base = 60 ft
Now, find the Slant Height (which is the height of one of the triangular faces):
Slant Height = sqrt((1/2 * side)^2 + height^2)
Slant Height = sqrt((1/2 * 15)^2 + 9.9^2)
Slant Height = sqrt(112.5 + 98.01)
Slant Height = sqrt(210.51)
Slant Height = 14.5 ft (approximately)
Finally, calculate the Surface Area:
Surface Area = 225 + (1/2) * 60 * 14.5
Surface Area = 225 + 435
Surface Area = 660 ft^2
So, after recalculation, the correct answer is:
660 ft.2
you have to use one of the answers
In that case, the closest answer from the options provided would be:
819 ft.2
Therefore, the correct answer to the question would be:
819 ft.2
?
Apologies for the oversight. Let's redo the calculations systematically and use one of the provided answer choices.
Given:
Side of base = 15 ft
Perpendicular height = 9.9 ft
Step 1: Calculate the Base Area
Base Area = side^2
Base Area = 15^2
Base Area = 225 sq. ft
Step 2: Calculate the Perimeter of the Base
Perimeter of Base = 4 * side
Perimeter of Base = 4 * 15
Perimeter of Base = 60 ft
Step 3: Calculate the Slant Height
Slant Height = sqrt((1/2 * side)^2 + height^2)
Slant Height = sqrt((1/2 * 15)^2 + 9.9^2)
Slant Height = sqrt((112.5) + 98.01)
Slant Height ≈ 14.25 ft
Step 4: Calculate Surface Area
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
Surface Area = 225 + (1/2) * 60 * 14.25
Surface Area = 225 + 427.5
Surface Area = 652.5 sq. ft
Among the provided answer choices, the closest one is 522 ft.2.
Therefore, the correct answer from the options provided would be:
522 ft.2