Unit Squares and Triangles
A nice problem that involves four geometric transformations.
Given: Three unit squares and two line segments connecting two pairs of vertices.
What is the area of △ELF?
Two solutions are given on the website below; this solution uses transformations, a CCSS feature.
Since △ELF ~ △HIF ≅ △EFA, and the length of side FH = √5,
then the area of △HIF = 5(△ELF) since area grows by the square of the scale factor.
Hence the area of △ELF = 0.2 units. There are four steps to the transformation:
1- reflect △ELF about line EF
2- rotate △ELF about point F
3- dilate △ELF about point F by factor of √5
4- translate △ELF 2 units down
- from https://www.illustrativemathematics.org/illustrations/918

1- Why are the three triangles similar?
2- Can you find the area of triangle ELF another way?