Name: Finding the Surface Area of a Square Pyramid- Middle School Math | 视频 | 干净世界
Uploaded: 2023-12-01T23:21:21.840Z
Duration: 3 min 15 s
Description: Geometry Teachers Never Spend Time Trying to Find Materials for Your Lessons Again! Join Our Geometry Teacher Community Today! http://geometrycoach.com/Geome... | 视频 | 干净世界

MooMooMath and Science

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In this video you will learn how to find the area of a square pyramid

Transcript
Hi welcome to MooMooMath
Today we are going to look at finding the total areaof a square pyramid, a square pyramid has an apex and the base is a square.
Let's look at one.
Here is our square pyramid, and the base is 10 on each side, and we have a height and the slant height which is from the apex to a point all the way down to the side of the base in the middle of the base.
This distance is what we need to find surface area.
Our formula is ( works like this)
There are two parts to the formula.
The first part is the lateral area. 
The lateral area is the triangles that go around the pyramid.
If take this and fold it out you will see that the lateral area is just four triangles. 
You could find the area of one triangle and just multiply by four and you would have the lateral area. 
There is an easier formula. For lateral area use 1/2 base times height, but instead of finding the area of one triangle we will find the area of four triangles which is the perimeter of the base and multiply it by your height, and in this case it is the slant height.
1/2 perimeter times height.
Let's find the perimeter first.
The perimeter of the base which is 10 on each side, so the perimeter is 10 x 4 = 40 and 1/2 of 40 times our slant height is given and that is 9 
We have 1/2 times forty times 9 = which equals 20 times 9 = 180 in square units.
So that gives us the lateral area of our pyramid.
That accounts for all four sides, now we need to account for the base.
Base of this pyramid equals side squared because the base is a square. 
The side of the base is 10 and 10 squared is 100.
How many bases do I have? Only 1 base
I will add 100 to 180 and that will give us 280 square units
The last part is take one lateral area plus base rea and that gives us the total surface area of the pyramid.
Hope the video was helpful.

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