Teaching Kids Programming – Compute the Area of Square in Square (Similar Triangles, Math, Geometry) | ninjasquad

**Teaching Kids Programming**: Videos on **Data Structures and Algorithms**

The shorter line segment on each side is 1, and the longer segment is 2. Thus the big square area is 3×3=9

### Compute the Area of Square in Square (Math, Geometry)

We want to calculate the “square” EFGH. The Shape of EFGH is a square. Angle BAE+EAD=90, Triangle ABF is similar to Triangle DAE, thus, Angle ADE=Angle BAF, thus We can prove Angle EAD+ADE=90, so, Angle E is 90 degree.

Then, we just have to calculate the area of Triangle AED, so the area size of EFGH=ABCD-4*DAE.

Another solution is to compute a side length of the inner square. We can compute the Side DH in Triangle CHD, and then subtract this from DEE, so we know one side of the inner square, and thus compute the area of the inner square by square one side.

### Determine Similar Triangles

Two triangles are similar by the following cases:

- AA: Two angles are the same.
- SSS: Three sides are proportional.
- SAS: Two sides are proportional and their corresponding angle is the same.
- For two right-angle triangles, longest side and one other side are proportional.
- For two right-angles triangle, another angle is the same.

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