## Wednesday, March 1, 2023

### Geometry Problem 1516: Finding the Length of a Side in an Equiangular Hexagon with Given Three Side Lengths. Difficulty Level: High School.

Geometry Problem 1516. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

More Details

To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

#### 3 comments:

1. https://photos.app.goo.gl/Gv5Rwt8cf4DriGjp6

2. Form equilateral Triangle LMN, L on AB extended, M on CD extended and N on EF extended. Let AF = NF = x and DE = EM = y

Since LN = MN,
x + 7 + 3 = x + 2 + y from which y = 8 = DE

Sumith Peiris
Moratuwa
Sri Lanka

3. Solution 2

It is easy to see that CD//AF and BC//EF.
Complete parallelogram with sides CDM, MEF, FAT, TBC

So TC = FM and so 7 + 3 = 2 + DE since Tr.s ABT and DEM are both equilateral
Hence DE = 8

Sumith Peiris
Moratuwa
Sri Lanka