Step-by-step explanation:
such problems are always the combination of areas of simple figures.
in our case here the simplest way seems to me to calculate the area of the whole 15×15 square (the side lengths are 15 and 9+6 = 15) and then subtract the small 6×6 square (top left), the small 6×3 triangle (bottom right) and the larger 6×9 triangle (top right).
we know that the left side of the main square is 9+6 = 15.
we know that the missing side piece (top right) is also 6 (like its left side). and the right side piece is 15-6-6 = 3.
that is how we know the side lengths of the missing pieces.
so,
15×15 = 225 cm²
the small square is
6×6 = 36 cm²
the large triangle is
6×9/2 = 3×9 = 27 cm²
the small triangle is
6×3/2 = 3×3 = 9 cm²
so, the total area of the figure is
225 - 36 - 27 - 9 = 153 cm²
