find the surface area of a square pyramind with a base length of 24cm and a height of 16cm . . . . . . . . A.1056 cm^2 . . . . . . . . . . B.1536 cm^2 . . . . . . . . . . C.816 cm^2 . . . . . . . . . . D.1344 cm^2(I CHOOSE THIS ONE)

I get 1536

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

1. Base Area:
The base of the pyramid is a square, so its area is given by the formula side^2. In this case, the base length is 24cm.
Base Area = 24cm * 24cm = 576cm^2

2. Lateral Faces:
Since the pyramid is a square pyramid, it has four identical triangular faces. To calculate the area of one triangular face, we need to find the area of the base of the triangle.
Base of the triangle = 24 cm
Height of the triangle = 16 cm

Area of one triangular face = (1/2) * Base * Height
= (1/2) * 24cm * 16cm
= 192cm^2

Total area of the four triangular faces = 4 * 192cm^2 = 768cm^2

3. Surface Area:
The surface area of the square pyramid is the sum of the base area and the total area of the lateral faces.
Surface Area = Base Area + Total area of lateral faces
= 576cm^2 + 768cm^2
= 1344cm^2

Therefore, the correct answer is D. 1344 cm^2.

To find the surface area of a square pyramid, you need to add the areas of all its faces.

1. Start by calculating the area of the base: Since the base is a square with a length of 24 cm, the area would be the length squared: 24 cm x 24 cm = 576 cm².

2. Next, find the area of the four triangular faces. Each triangular face can be considered a right triangle:

a. The base of each triangle corresponds to the side length of the square base of the pyramid, which is 24 cm.

b. The height of each triangle is the same as the overall height of the pyramid, which is 16 cm.

c. Apply the formula for the area of a triangle: 1/2 x base x height.

d. Calculate the area of one triangle: 1/2 x 24 cm x 16 cm = 192 cm².

e. Since there are four triangular faces, multiply the area of one triangle by 4: 192 cm² x 4 = 768 cm².

3. Finally, add the area of the base and the area of the four triangular faces together: 576 cm² (base) + 768 cm² (triangular faces) = 1344 cm².

Therefore, the correct answer is D. 1344 cm².