(i) After naming the figure In rectangle ABCD, Area of rectangle = Length × Breadth 7 × BC = 21 ⇒ BC = 3 in ∴ AF = AD + DF = 3 in + 4 in = 7 in In the rectangle EFAG, EF × AF = 28 in 2 ⇒ EF × 7 in = 28 in 2 ⇒ EF = 4 in ∴ HA = HG + GA = 3 in + 4 in = 7 in In rectangle HIJA, Area = HA × AJ ⇒ 35 in 2 = 7 in × AJ ⇒ AJ = 5 in ∴ AK = AJ + JK = 5 in + 2 in = 7 in In rectangle KLMA, Area = KL × LM ⇒ x in × 7 in = 14 in 2 ⇒ x = 2 in Thus, the missing sidelength = 2 in (ii) After naming the figure, In rectangle ABGH, Area = AB × AH AB × 4 m = 29 m² AB = \(\frac {29}{4}\) m or 7.25 m Area of rectangle HGDC = Area of rectangle ABDC – Area of rectangle ABGH = 50 m 2 – 29 m 2 = 21 m 2 In rectangle HGDC, CD × GD = 21 m 2 ⇒ \(\frac {29}{4}\)m × GD = 21 m 2 ⇒ GD = \(\frac {84}{29}\) m or 2.9 m In rectangle BEFG, BG × BE = 11 m 2 ⇒ 4 m × M = 11 m 2 ⇒ BE = \(\frac {11}{4}\)m or 2.75 m Thus, AB = \(\frac {29}{4}\) m; BE = \(\frac {11}{4}\) m and GD = \(\frac {84}{29}\) m