Find the surface area of a square pyramid with side length 2 m and slant height 2 m
Well, a square pyramid is a unique shape, just like a clown's nose! To find the surface area, we'll need to break it down into its different parts.
First, let's calculate the area of the base. Since it's a square pyramid, the base is just a square with side length 2 m. The area of a square is given by the formula A = side length squared, so in this case, the base area is 2 m * 2 m = 4 m².
Now, let's tackle the lateral faces. Each lateral face is a triangle, with a base that equals the side length (2 m) and a height equal to the slant height (2 m). The formula for the area of a triangle is 1/2 * base * height, so in this case, the area of each lateral face is 1/2 * 2 m * 2 m = 2 m².
Since there are 4 identical triangular faces in a square pyramid, the total area for all the lateral faces is 4 * 2 m² = 8 m².
Now, to find the surface area, we sum the base area and the area of the lateral faces: 4 m² (base area) + 8 m² (lateral face area) = 12 m².
So, the surface area of the square pyramid is 12 square meters. Voila!
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of each triangular face.
1. Area of the base:
The base of a square pyramid is a square, so we can find the area by squaring the length of one side.
Given that the side length is 2 meters, the area of the base is 2^2 = 4 square meters.
2. Area of each triangular face:
The slant height is the height of each triangular face. To calculate the area of each triangular face, we can use the formula: A = (1/2) * base * height.
The base length is equal to the side length of the square, which is 2 meters.
The height can be calculated using the Pythagorean theorem: h = √(slant height^2 - base^2).
In this case, the slant height is also 2 meters.
Plugging these values into the formula, the height of each triangular face is h = √(2^2 - 2^2) = 0 meters.
Since the height is 0 meters, the area of each triangular face is also 0 square meters.
3. Calculate the surface area:
The surface area of a square pyramid is the sum of the area of the base and the areas of the triangular faces.
Surface area = area of the base + total area of all triangular faces
Surface area = 4 square meters + (0 square meters × 4 faces)
Surface area = 4 square meters
Therefore, the surface area of a square pyramid with side length 2 meters and slant height 2 meters is 4 square meters.
To find the surface area of a square pyramid, you need to calculate the area of all its individual faces and then add them together.
Here's a step-by-step explanation to find the surface area of a square pyramid with a side length of 2 m and slant height of 2 m:
1. Start by calculating the area of the base. Since it's a square pyramid, the base is a square. Given that the side length of the square is 2 m, you can simply use the formula for the area of a square: A = s^2, where s is the length of a side.
So, the area of the base = 2 m * 2 m = 4 m^2.
2. Next, calculate the area of each triangular face. You need to find the area of four triangles since a square pyramid has four identical triangular faces.
To calculate the area of a triangle, you can use the formula: A = 1/2 * base * height. In this case, the base of each triangle is the side length of the square, which is 2 m. The height of the triangle is given as the slant height, which is also 2 m.
So, the area of each triangular face = 1/2 * 2 m * 2 m = 2 m^2.
3. Since there are four identical triangular faces, you need to multiply the area of a single triangular face by 4 to get the total area of all four.
Total area of the triangular faces = 4 * 2 m^2 = 8 m^2.
4. Finally, to get the surface area of the square pyramid, you add the area of the base and the total area of the triangular faces:
Surface area = area of base + total area of triangular faces = 4 m^2 + 8 m^2 = 12 m^2.
Therefore, the surface area of the square pyramid with a side length of 2 m and slant height of 2 m is 12 square meters (m^2).
Find the surface area of a square pyramid with side length 1 in and slant height 5 in.
base: 2^2
each of 4 faces: (2*2)/2
so crank it out