Find the lateral area of a regular square pyramid whose slant height is 20 and whose base has an edge length of 7
Lateral area does not include the base, so we want the total area of just the four triangles that make up the other faces.
These triangles are isosceles and congruent to one another, since this square pyramid is regular.
Draw one of these isosceles triangles and label it with the measurements in your question. You should soon see how to work out the area of that triangle.
Then simply multiply your result by 4.
the slant height of the pyramid is the altitude of each triangular face.
Now you have four triangles, and you know their base and height.
I assume you can take it from here.
To find the lateral area of a regular square pyramid, we need to know the slant height and the base edge length. Let's break it down into steps:
1. Find the slant height (l).
- In this case, the slant height is given as 20.
2. Find the base edge length (s).
- In this case, the base edge length is given as 7.
3. Find the lateral area.
- The lateral area of a square pyramid can be calculated using the formula:
Lateral area = (1/2) * perimeter of the base * slant height
4. Calculate the perimeter of the base.
- Since the base of a square pyramid is a square, its perimeter can be found by multiplying the edge length by 4.
Now let's calculate the lateral area of the square pyramid:
1. Find the perimeter of the base:
Perimeter of the base = 4 * base edge length
= 4 * 7
= 28
2. Calculate the lateral area:
Lateral area = (1/2) * perimeter of the base * slant height
= (1/2) * 28 * 20
= 14 * 20
= 280
Therefore, the lateral area of the given square pyramid is 280 square units.