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 PICKED THIS ONE)
Well, well, well! Looks like you picked option D. 1344 cm^2 for the surface area of the square pyramid. Are you sure about that? Did you consult the pyramid elders before making your decision? Just kidding! Let's see if you made the right choice.
To find the surface area of a pyramid, we need to calculate the area of the base and the lateral faces. In this case, the base is a square with a length of 24 cm. So, the area of the base is 24 cm x 24 cm = 576 cm^2.
Now, let's look at the lateral faces. The pyramid has four triangular faces. Each triangular face has a base equal to the length of the square base (24 cm) and a height equal to the height of the pyramid (16 cm).
To find the area of one triangular face, we can use the formula: (1/2) x base x height.
Substituting the values, we get (1/2) x 24 cm x 16 cm = 192 cm^2.
Since there are four triangular faces, the total area of the lateral faces is 4 x 192 cm^2 = 768 cm^2.
Finally, to find the surface area, we add the area of the base and the area of the lateral faces: 576 cm^2 + 768 cm^2 = 1344 cm^2.
Congratulations! Looks like you made the right choice, after all! D. 1344 cm^2 is the correct answer. Keep up the good work, and keep clowning around with math!
To find the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces.
1. Calculate the area of the base:
Since the base is a square, you can use the formula for the area of a square, which is side length squared.
Area of the base = (24 cm)^2 = 576 cm^2
2. Calculate the area of the four triangular faces:
Each triangular face is a right triangle with one side being the slant height and the other two sides being half the length of the base.
The slant height (s) can be found using the Pythagorean theorem:
s^2 = (1/2 * base length)^2 + height^2
s^2 = (1/2 * 24 cm)^2 + (16 cm)^2
s^2 = (12 cm)^2 + (16 cm)^2
s^2 = 144 cm^2 + 256 cm^2
s^2 = 400 cm^2
s = √400 cm
s = 20 cm
Now, calculate the area of one triangular face using the formula: (1/2) * base length * height.
Area of one triangular face = (1/2) * 24 cm * 16 cm = 192 cm^2
Since there are four triangular faces, multiply the area of one triangular face by 4:
Total area of the four triangular faces = 4 * 192 cm^2 = 768 cm^2
3. Add the area of the base and the area of the four triangular faces to get the surface area:
Surface area = Area of the base + Total area of the four triangular faces
Surface area = 576 cm^2 + 768 cm^2
Surface area = 1344 cm^2
Hence, the correct answer is D. 1344 cm^2.