Use a formula to find the surface area of the square pyramid.

A pyramid labeled with a height of 6 feet and base of 3 feet.
A. 45 ft2
B. 81 ft2
C. 36 ft2
D. 72 ft2

so, did you use your formula?

What did you get?

45 ft

To find the surface area of a square pyramid, you can use the formula:

Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)

In this case, the base of the square pyramid is a square with sides of length 3 feet.

1. First, calculate the area of the base. Since the base is a square, you can use the formula for the area of a square:

Base Area = (side length)²
Base Area = 3²
Base Area = 9 square feet

2. Next, calculate the perimeter of the base. Since the base is a square, all sides are equal, and the perimeter can be found by multiplying the side length by 4:

Perimeter of Base = side length x 4
Perimeter of Base = 3 x 4
Perimeter of Base = 12 feet

3. Finally, find the slant height of the pyramid. The slant height is the height of one of the triangular faces. Since the pyramid is labeled to have a height of 6 feet, the slant height can be found using the Pythagorean theorem.

Using the base side length of 3 feet, the slant height (s) can be found by:

s² = 3² + 6²
s² = 9 + 36
s² = 45
s = √45
s ≈ 6.7082 feet

Now, substitute the values into the formula for surface area:

Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
Surface Area = 9 + (0.5 x 12 x 6.7082)
Surface Area ≈ 9 + (0.5 x 12 x 6.7082)
Surface Area ≈ 9 + 40.2492
Surface Area ≈ 49.2492 square feet

Therefore, the surface area of the square pyramid with a height of 6 feet and base of 3 feet is approximately 49.2492 square feet.

None of the provided answer options match the calculated surface area, so the correct answer is not given.

To find the surface area of a square pyramid, you need to calculate the area of the base and the lateral faces, and then add them together.

First, let's find the area of the base. In this case, the base is a square with a side length of 3 feet. The formula to find the area of a square is A = s^2, where A is the area and s is the length of a side.

So, the area of the base is 3^2 = 9 square feet.

Next, let's find the area of the lateral faces. Each lateral face of a square pyramid is a triangle, with two sides that are slant heights and the base as the side length of the square.

To find the slant height, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle, with one leg being the height of the pyramid (6 feet) and the other leg being half of the base length (3/2 = 1.5 feet).

Using the Pythagorean theorem: slant height^2 = height^2 + (1/2 * base length)^2.

Substituting the values: slant height^2 = 6^2 + 1.5^2 = 36 + 2.25 = 38.25.
So, the slant height is the square root of 38.25, which is approximately 6.18 feet (rounded to two decimal places).

Now, we can calculate the area of each lateral face using the formula for the area of a triangle, which is A = (1/2) * base * height.

The base of each triangle is the side length of the square (3 feet), and the height is the slant height (6.18 feet).

Therefore, the area of each lateral face is (1/2) * 3 * 6.18 = 9.27 square feet.

Since there are 4 lateral faces on a square pyramid, the total area of the lateral faces is 4 * 9.27 = 37.08 square feet.

Finally, to find the total surface area, add the area of the base and the area of the lateral faces: 9 + 37.08 = 46.08 square feet.

Therefore, the correct answer is not among the options given. The correct answer is 46.08 ft^2.