Notice that 9 x 9 = 81 , and 6 x 6 = 36
81 + 36 = 117

Or

Notice that 117 = 13 x 3 x 3

So we can form 13 small squares , each 3cm.

We can arrange them into two bigger squares, one made of four 3cm squares,
(2 small squares by 2 small squares)

and the other made of nine 3cm squares.


Length of the biggest square = 3cm x 3 = 9cm

Length of the middle square = 3cm x 2
= 6cm






FH = HI

Since HI = HG ,(both are sides of the same square)

Then FH = HG

So FG = 2HG

Since FG = 6cm, (see working above)
HG = 6cm ÷ 2 = 3cm

so the smallest square is 3cm by 3cm

Length of DJ = DC + CG + GJ
= 9cm + 6cm + 3cm = 18cm

Area of triangle of ADJ = ½ x AD x DJ
= ½ x 18cm x 9cm
= 81cm²