Find the surface area and the lateral area of a regular square pyramid with base edge 6 and a lateral edge √34. PLEASE PLEASE HUHU Teach me how and what is lateral edge
lateral edge is an edge from the base to the vertex. As opposed to a base edge.
If the base edge is 6, the base diagonal is 6√2
Now draw a right triangle from the center of the base to the vertex, including one base corner.
(6√2/2)^2 + h^2 = (√34)^2
18 + h^2 = 34
h = 4
So, now we have height 4 and base edge 6, so the faces are triangles with
base = 6
height = √(3^2 + 4^2) = 5
lateral area is thus 4 * 1/2 (6)(5)
add the square base if desired.
18.63
idk lol
To find the surface area and the lateral area of a regular square pyramid, we need to understand what the lateral edge is and how to calculate it.
In a pyramid, the lateral edges are the edges that connect the apex (top vertex) of the pyramid to the vertices of the base. These edges form the triangular faces of the pyramid.
Now let's calculate the lateral edge of the given square pyramid. We are given that the lateral edge is √34.
To calculate the surface area of a square pyramid, we need to find the sum of the areas of all its faces.
Surface Area of a Square Pyramid:
1. The base of the pyramid is a square, so the area of the base is calculated as 6 * 6 = 36 square units.
2. There are four triangular faces. Since the base is a square, all the triangular faces are congruent.
To find the area of one triangular face, we'll use the formula for the area of a triangle, which is 1/2 * base * height.
In our case, the base of the triangular face is one side of the square base, which is 6, and the height is the lateral edge (√34).
Area of one triangular face: 1/2 * 6 * √34 = 3√34 square units.
Since there are four triangular faces, the total area of all the triangular faces is 4 * 3√34 = 12√34 square units.
Total Surface Area: 36 (base) + 12√34 (triangular faces) = 36 + 12√34 square units.
To find the lateral area of the pyramid, we only need to consider the triangular faces.
Lateral Area: 12√34 square units.
Therefore, the surface area of the given pyramid is 36 + 12√34 square units, and the lateral area is 12√34 square units.