Find the lateral area for the square pyramid.

Height: 22
Base: 8
Side: 8

I know the answer, I just want someone to show me how to actually calculate it to find the answer.

Thanks :)

the lateral area consists of 4 isosceles triangle faces.

the side length of the pyramid is the base of each face.

The slant height of the pyramid is the altitude of each face.

Looking sideways into the pyramid, the slant height is the hypotenuse of a right triangle whose base is 1/2 the side of the pyramid, and whose height is the height of the pyramid. so, the slant height s is

s^2 = 4^2 + 22^2
s = √500

so, the area of each face is 1/2 bh = 4√500 = 40√5

the lateral area of the pyramid is thus 160√5

To find the lateral area of a pyramid, you need to calculate the total area of the triangular faces that make up the sides of the pyramid.

Step 1: Start by calculating the area of one triangular face.

The base of the triangle is equal to the length of the side of the pyramid, which is given as 8.

The height of the triangle can be found using the Pythagorean theorem. Since the triangle is a right triangle, with one side being the height of the pyramid (given as 22) and the other side being half the base (4), we can find the height (h) using the equation:

h^2 = 22^2 - 4^2

h^2 = 484 - 16

h^2 = 468

h ≈ √468

h ≈ 21.63

Step 2: Calculate the area of the triangular face using the formula for the area of a triangle:

Area = (1/2) * base * height

Area = (1/2) * 8 * 21.63

Area ≈ 86.52

Step 3: Multiply the area of one triangular face by the number of triangular faces on the pyramid. A square pyramid has 4 triangular faces.

Lateral Area = 4 * 86.52

Lateral Area ≈ 346.08

Therefore, the lateral area of the square pyramid is approximately 346.08 square units.

To find the lateral area of a square pyramid, you need to calculate the sum of the areas of all the lateral faces.

Here's how you can calculate it step by step:

1. Identify the lateral faces of the square pyramid. In this case, there are four triangular lateral faces.

2. Calculate the area of one triangular lateral face. The area of a triangle can be found using the formula A = (1/2) * base * height, where the base is the length of the side of the square base, and the height is the height of the pyramid. In this case, the base is 8 and the height is 22. So the area of one triangular lateral face is A = (1/2) * 8 * 22.

3. Multiply the area of one triangular lateral face by the number of lateral faces. Since there are four triangular lateral faces, multiply the area by 4.

4. Calculate the lateral area by multiplying the area of one triangular lateral face by the number of lateral faces. In this case, the lateral area of the square pyramid is (1/2) * 8 * 22 * 4.

5. Simplify the expression to find the final answer. In this case, the lateral area is 352.

So, the lateral area of the given square pyramid is 352 square units.