Use the formula for the surface area of a square pyramid to find the surface area if the base edge length is 5 yards and the height is 25 yards. Round to the nearest whole number.(1 point)
The surface area of a square pyramid can be found using the formula:
Surface Area = (base area) + (1/2) * (perimeter of base) * (slant height)
To find the base area of the square pyramid, we need to find the area of the base, which is a square with side length 5 yards. The formula for the area of a square is:
Area = side length^2
So, the base area = 5^2 = 25 square yards.
To find the perimeter of the base, we multiply the side length by 4 since a square has 4 equal sides. Therefore, the perimeter of the base is:
Perimeter = 4 * side length = 4 * 5 = 20 yards.
The slant height can be found using the Pythagorean theorem, since we have a right triangle with the height (25 yards) and the half of the base (2.5 yards) as the legs and the slant height as the hypotenuse. The Pythagorean theorem states:
c^2 = a^2 + b^2
where c is the hypotenuse (slant height) and a and b are the legs. Rearranging the equation, we have:
c = sqrt(a^2 + b^2)
Using the numbers, the slant height = sqrt(25^2 + 2.5^2) = sqrt(625 + 6.25) = sqrt(631.25) ≈ 25.106 yards.
Now, we can substitute the values into the surface area formula:
Surface Area = 25 + (1/2) * 20 * 25.106
Surface Area ≈ 25 + 10 * 25.106
Surface Area ≈ 25 + 251.06
Surface Area ≈ 276.06
Rounding to the nearest whole number, the surface area of the square pyramid is 276 square yards.
What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.?(1 point)
The surface area of a square pyramid can be found using the formula:
Surface Area = (base area) + (1/2) * (perimeter of base) * (slant height)
To find the base area of the square pyramid, we need to find the area of the base, which is a square with side length 8 ft. The formula for the area of a square is:
Area = side length^2
So, the base area = 8^2 = 64 square feet.
To find the perimeter of the base, we multiply the side length by 4 since a square has 4 equal sides. Therefore, the perimeter of the base is:
Perimeter = 4 * side length = 4 * 8 = 32 ft.
Given that the slant height is 16 ft., we can now substitute the values into the surface area formula:
Surface Area = 64 + (1/2) * 32 * 16
Surface Area = 64 + 256
Surface Area = 320 square feet
The surface area of the square pyramid is 320 square feet.
A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid. The pyramid has a base of 5 in., the height of the base is 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid. (1 point)
The correct formula to find the surface area of a triangular pyramid is:
Surface Area = (base area) + (1/2) * (perimeter of base) * (slant height)
To find the base area of the triangular pyramid, we need to find the area of the base, which is a triangle. The formula for the area of a triangle is:
Area = (1/2) * base * height
Given that the base of the pyramid is 5 in. and the height of the base is 4.3 in., we can calculate the base area:
Base Area = (1/2) * 5 * 4.3
Base Area = 10.75 square inches
To find the perimeter of the base, we need to know the length of all three sides of the triangle. But we are only given the length of the base, which is 5 in.
Since we don't have enough information to find the perimeter, it is not possible to calculate the surface area of the chocolate pyramid with the given information.
When creating the formula for surface area of a triangular pyramid (SA=12ab+3(12lb)) , what formula is being used?(1 point)
The formula being used for the surface area of a triangular pyramid is:
SA = 12 * (area of each triangular face) + 3 * (area of the triangular base)
This formula takes into account the fact that a triangular pyramid has a triangular base and three triangular faces. The formula calculates the surface area of each triangular face (12 * (area of each triangular face)) and adds it to three times the area of the triangular base (3 * (area of the triangular base)) to find the total surface area of the triangular pyramid.
answer?
The formula being used for the surface area of a triangular pyramid is:
SA = 12ab + 3(12lb)
This formula calculates the surface area of a triangular pyramid by multiplying the base length (b) and base width (a) by 12 and adding to it three times the product of the base length (b) and slant height (l) multiplied by 12.
volume
volume area of a square
area of a triangle
perimeter