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## Geometry (all content)

### Course: Geometry (all content)>Unit 4

Lesson 5: Angle bisectors

Showing that area is equal to inradius times semiperimeter. Created by Sal Khan.

## Want to join the conversation?

• So just to clarify from the triangles height is R?
• for each small triangle in the first triangle, the height is R and the base is one of the sides. But we don't know the height of the first triangle, so we want to find the height of the smaller triangles inside it.
• So is the formula "r * p / 2" another way to find the area of a triangle?
• Yes, if you know r and p.

It is more useful to determine the inradius r from the area and the perimeter.
• According to my textbook you can find the inradius 'r' of a triangle with formula r=A/s, where A=area of triangle and s= semiperimeter, Is this true??
• Yes because if r * s (aka Perimeter/2) is equal to A, then A/r=s, and A/s=r
• What would we use this in our everyday lives (besides teaching others it because it is just cool to teach people about things they don't know)? I don't really know why we would need this in our everyday lives...
(1 vote)
• Well, if you're working on anything that's triangular shaped (maybe a table, maybe a patio, maybe a field, maybe even a city!) and you want to place something in the center so that is equally distanced and easy to access from all sides of the triangle - they do, or at least did, this a lot with churches and city halls - you're gonna be using the incenter! Lots of stuff are triangles just because they're so easy to work with and have a lot of different utilities!
• This video references a concept at (Pythagorean Theorem) not addressed yet as if I follow the knowledge map. Should I be following another path to get to this concept?
• In my opinion, it is better to follow the playlists in order on each subject than to use the knowledge map.
• If the inradius divides the sides of the triangle (ab,bc,ca) into the ratios m1:n1, m2:n2, m3:n3 respectively, how can I find the lengths of the sides ab, bc and ca? The area is also not provided.
:(
• So, would the diameter of that circle be called the indiameter?
• Well I don't think there's something like indiameter and the diameter isn't included in any of the properties (acc to me) so forget about the diameter
(1 vote)
• Suggestion: perhaps add some simple questions or reviews to the more empty spaces in the triangle theory? It doesent have to be difficult, it just gets slightly tedious, and I feel that I retain information much better that way.

The theories expressed here are great, and Sahls speech is very condensed- its just the gamified learning that really "sets it in stone" for me mentally.