Find the surface area of a square pyramid with a base length of 24 cm and height of 16 cm
1. 1056 cm2
2. 1536 cm2
3. 816 cm2
4. 1344 cm2
The formula for the surface area of a square pyramid is:
Surface Area = Base Area + (1/2 x Perimeter of Base x Slant Height)
First, let's find the base area:
Base Area = (length of base)^2 = 24^2 = 576 cm^2
Next, let's find the slant height. We can use the Pythagorean theorem, since we know the height (16 cm) and half the length of the base (12 cm):
slant height^2 = height^2 + (1/2 x length of base)^2
slant height^2 = 16^2 + 12^2
slant height^2 = 256 + 144
slant height^2 = 400
slant height = 20 cm
Now we can plug in the values to find the surface area:
Surface Area = 576 + (1/2 x 4 x 20 x 24)
Surface Area = 576 + 960
Surface Area = 1536 cm^2
Therefore, the answer is option 2.
To find the surface area of a square pyramid, you need to calculate the area of the base and the areas of four triangular faces.
1. Start by calculating the area of the base:
The base is a square, so the formula is A = s², where s is the length of one side.
A = 24 cm × 24 cm = 576 cm²
2. Next, calculate the area of each triangular face:
Since it's a square pyramid, all four triangular faces will have the same dimensions.
The formula to calculate the area of a triangle is A = 1/2 × base × height.
For each triangular face, the base length is the same as the length of one side of the square base, which is 24 cm.
The height is the height of the pyramid, which is 16 cm.
A = 1/2 × 24 cm × 16 cm = 192 cm²
3. Since there are four triangular faces, multiply the area of one triangular face by 4 to find the total area of all four faces.
Total area of the triangular faces = 4 × 192 cm² = 768 cm²
4. Finally, add the area of the base and the total area of the four triangular faces to find the total surface area.
Total surface area = Area of base + Total area of triangular faces
= 576 cm² + 768 cm²
= 1344 cm²
Therefore, the correct answer is option 4. 1344 cm².