Find the surface area of a square pyramid with a base length of 24 cm and a height of 16 cm.
A.) 1056 cm²
B.) 1536 cm²
C.) 816 cm²
D.) 1344 cm²
B.) 1536 cm²
Well, since you're looking for the surface area of a square pyramid, let's break it down. The surface area of a square pyramid is equal to the sum of the areas of its base and its four triangular faces. So, let's calculate!
First, let's find the area of the base. Since it's a square pyramid with a base length of 24 cm, we can use the formula for the area of a square: side length squared. In this case, it's 24 cm × 24 cm, which gives us a base area of 576 cm².
Next, let's find the area of the triangular faces. Each triangular face will have a base equal to the length of one side of the square base, so they will all be 24 cm. The height of each triangle is the same as the height of the pyramid, which is 16 cm. Using the formula for the area of a triangle: base × height ÷ 2, we can calculate the area of one triangle: (24 cm × 16 cm) ÷ 2 = 192 cm². Since there are 4 triangular faces on this pyramid, the total area of all the triangular faces is 4 × 192 cm² = 768 cm².
Now, let's add up the area of the base and the area of the triangular faces to find the total surface area: 576 cm² (base) + 768 cm² (triangular faces) = 1344 cm².
So, the surface area of the square pyramid is 1344 cm². Looks like the answer is D.) 1344 cm².
To find the surface area of a square pyramid, we need to calculate the area of the base and the lateral faces.
1. Calculate the area of the base:
The base of the square pyramid is a square, so we can find its area by squaring the length of one side.
Area of the base = (side length)² = (24 cm)² = 576 cm²
2. Calculate the area of the lateral faces:
A square pyramid has 4 identical triangular faces as its lateral faces. To find the area of one triangular face, we can use the formula: (base × height) / 2.
Area of one triangular face = (24 cm × 16 cm) / 2 = 384 cm²
Since there are 4 identical triangular faces, we multiply the area by 4.
Area of all the lateral faces = 384 cm² × 4 = 1536 cm²
3. Calculate the total surface area:
Total surface area = area of the base + area of all the lateral faces
Total surface area = 576 cm² + 1536 cm² = 2112 cm²
Therefore, the correct answer is not listed.
To find the surface area of a square pyramid, we need to calculate the area of each individual face and then add them together.
The square pyramid has five faces: one square base and four triangular faces.
1. To find the area of the base, we use the formula for the area of a square: Area = side length^2. In this case, the base length is given as 24 cm, so the area of the base is 24^2 = 576 cm².
2. To find the area of each triangular face, we use the formula for the area of a triangle: Area = (1/2) x base length x height. In this case, the base length is 24 cm (the same as the base length of the square) and the height is given as 16 cm. Therefore, the area of each triangular face is (1/2) x 24 cm x 16 cm = 192 cm².
Since there are four triangular faces, the total area of the triangular faces is 4 x 192 cm² = 768 cm².
To find the surface area of the square pyramid, we add the area of the base to the total area of the triangular faces: 576 cm² + 768 cm² = 1344 cm².
Therefore, the correct answer is D.) 1344 cm².