Count the number of squares in the given figure.

Concept: In a compound geometric figure, count squares by classifying every closed quadrilateral according to how many elementary regions (the smallest triangles or cells created by the grid and diagonal lines) combine to form it, checking at each step that all four sides are equal and all angles are right angles - not just any four-sided outline. Summing the counts across every size class gives the total number of squares in the figure.

Application: Applying this to the labelled figure above:

• Squares built from two triangular components each: ABKJ, BCLK, CDEL, LEFG, KLGH and JKHI - 6 squares.

• Squares built from four components each: CEGK - 1 square.

• Squares built from eight components each (spanning one full half of the rectangle): ACGI and BDFH - 2 squares.

Adding every size class: 6 + 1 + 2 = 9.

Cross-check: Listing every square found - ABKJ, BCLK, CDEL, LEFG, KLGH, JKHI, CEGK, ACGI and BDFH - gives exactly nine distinct squares with no shape repeated and none omitted, confirming the tally independently.

Result: Hence, the figure contains 9 squares.