The formula for the surface area of a square pyramid is given by:
SA = (1/2) × base perimeter × slant height + base area
In this case, the base length is 40 in and the surface area is 2800 in². Let's assume the slant height as "s".
The base perimeter of a square is given by: P = 4 × length of a side
In this case, the base perimeter is P = 4 × 40 = 160 in.
Now, we can substitute these values in the formula and solve for the slant height:
2800 = (1/2) × 160 × s + (40 × 40)
2800 = 80s + 1600 + 1600
2800 - 3200 = 80s
-400 = 80s
s = -400 / 80
s = -5
Therefore, the slant height is -5 in. However, a slant height cannot be negative. This indicates that there may be an error in the given information or calculation, or the square pyramid may not exist. Please double-check the measurements and try again.
Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in and SA equals 2,800 in.
11 answers
Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in and SA equals 2,800 in^2.
The formula for the surface area of a square pyramid is given by:
SA = (1/2) × base perimeter × slant height + base area
In this case, the base length is 40 in and the surface area is 2800 in². Let's assume the slant height as "s".
The base perimeter of a square is given by: P = 4 × length of a side
In this case, the base perimeter is P = 4 × 40 = 160 in.
Now, we can substitute these values in the formula and solve for the slant height:
2800 = (1/2) × 160 × s + (40 × 40)
2800 = 80s + 1600
80s = 2800 - 1600
80s = 1200
s = 1200 / 80
s = 15
Therefore, the slant height is 15 in.
SA = (1/2) × base perimeter × slant height + base area
In this case, the base length is 40 in and the surface area is 2800 in². Let's assume the slant height as "s".
The base perimeter of a square is given by: P = 4 × length of a side
In this case, the base perimeter is P = 4 × 40 = 160 in.
Now, we can substitute these values in the formula and solve for the slant height:
2800 = (1/2) × 160 × s + (40 × 40)
2800 = 80s + 1600
80s = 2800 - 1600
80s = 1200
s = 1200 / 80
s = 15
Therefore, the slant height is 15 in.
What is the surface area of a square pyramid where the base edge is 8ft. and the slant height is 16 ft.?
To find the surface area of a square pyramid, we can use the following formula:
SA = 2 × base area + base edge × slant height
First, we need to calculate the base area. The area of a square base is given by:
Base area = length of side × length of side
In this case, the base edge is 8 ft, so the base area is:
Base area = 8 ft × 8 ft = 64 ft²
Now, we can substitute the values into the surface area formula:
SA = 2 × 64 ft² + 8 ft × 16 ft
SA = 128 ft² + 128 ft
SA = 256 ft²
Therefore, the surface area of the square pyramid is 256 ft².
SA = 2 × base area + base edge × slant height
First, we need to calculate the base area. The area of a square base is given by:
Base area = length of side × length of side
In this case, the base edge is 8 ft, so the base area is:
Base area = 8 ft × 8 ft = 64 ft²
Now, we can substitute the values into the surface area formula:
SA = 2 × 64 ft² + 8 ft × 16 ft
SA = 128 ft² + 128 ft
SA = 256 ft²
Therefore, the surface area of the square pyramid is 256 ft².
What is the surface area of a square pyramid where the base edge is 5 yards and the slant height is 25 ft.? Round to the nearest whole number.
To find the surface area of a square pyramid, we can use the following formula:
SA = base area + lateral area
The base area of a square pyramid is given by:
Base area = (base edge)^2
In this case, the base edge is 5 yards, so the base area is:
Base area = (5 yards)^2 = 25 square yards
The lateral area of a square pyramid is given by:
Lateral area = (base edge)(slant height)/2
In this case, the base edge is 5 yards and the slant height is 25 ft. We need to convert the slant height to yards:
25 ft = 25/3 = 8.333... yards (rounded to 3 decimal places)
Now, we can calculate the lateral area:
Lateral area = (5 yards)(8.333... yards)/2 = 20.833... square yards
Finally, we can find the surface area:
SA = 25 square yards + 20.833... square yards ≈ 45.83 square yards
Rounding to the nearest whole number, the surface area of the square pyramid is 46 square yards.
SA = base area + lateral area
The base area of a square pyramid is given by:
Base area = (base edge)^2
In this case, the base edge is 5 yards, so the base area is:
Base area = (5 yards)^2 = 25 square yards
The lateral area of a square pyramid is given by:
Lateral area = (base edge)(slant height)/2
In this case, the base edge is 5 yards and the slant height is 25 ft. We need to convert the slant height to yards:
25 ft = 25/3 = 8.333... yards (rounded to 3 decimal places)
Now, we can calculate the lateral area:
Lateral area = (5 yards)(8.333... yards)/2 = 20.833... square yards
Finally, we can find the surface area:
SA = 25 square yards + 20.833... square yards ≈ 45.83 square yards
Rounding to the nearest whole number, the surface area of the square pyramid is 46 square yards.
A pastry chef is creating a chocolate desert in the shape of a triangular pyramid. The pyramid has a base of 5 in., the height has a base of 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid.
To find the surface area of a triangular pyramid, we can use the following formula:
SA = (base area) + (lateral area)
The base area of a triangular pyramid is given by:
Base area = (1/2) × base × height
In this case, the base is 5 in and the height is 4.3 in. We can substitute these values into the formula:
Base area = (1/2) × 5 in × 4.3 in = 10.75 in²
The lateral area of a triangular pyramid is given by:
Lateral area = (perimeter of base) × (slant height) / 2
In this case, the perimeter of the base of the triangular pyramid is the sum of all three sides, which is 5 in + 5 in + 5 in = 15 in. Let's substitute the values into the formula:
Lateral area = (15 in) × (6 in) / 2 = 45 in²
Now, we can find the surface area by adding the base area and the lateral area:
SA = 10.75 in² + 45 in² = 55.75 in²
Therefore, the surface area of the chocolate pyramid is approximately 55.75 in².
SA = (base area) + (lateral area)
The base area of a triangular pyramid is given by:
Base area = (1/2) × base × height
In this case, the base is 5 in and the height is 4.3 in. We can substitute these values into the formula:
Base area = (1/2) × 5 in × 4.3 in = 10.75 in²
The lateral area of a triangular pyramid is given by:
Lateral area = (perimeter of base) × (slant height) / 2
In this case, the perimeter of the base of the triangular pyramid is the sum of all three sides, which is 5 in + 5 in + 5 in = 15 in. Let's substitute the values into the formula:
Lateral area = (15 in) × (6 in) / 2 = 45 in²
Now, we can find the surface area by adding the base area and the lateral area:
SA = 10.75 in² + 45 in² = 55.75 in²
Therefore, the surface area of the chocolate pyramid is approximately 55.75 in².
When creating the formula for surface area of a triangular pyramid, what formula is being used?
A. perimeter
B. area of a triangle
C. area of a square
D. volume
A. perimeter
B. area of a triangle
C. area of a square
D. volume
The formula for the surface area of a triangular pyramid involves the concepts of a triangle and perimeter, so the correct answer is:
A. Perimeter
A. Perimeter