Question

Calculate the area of each one of the shaded regions given below (all measures are given in cm):
Figure

Answer 1

(i) Area of square BCDE= (Side)²
= (CD)²
= (3)² cm²
= 9 cm²
Area of rectangle ABFK = $\mathrm{Length}\times \mathrm{Breadth}$
= AK$\times$AB [(AB = AC − BC) and (AK = AL + LK)
= (5$\times$1) cm²
= 5 cm²

Area of rectangle MLKG = $\mathrm{Length}\times \mathrm{Breadth}$
= ML $\times$ MG
= (2 $\times$ 3) cm²
= 6 cm²
Area of rectangle JHGF= $\mathrm{Length}\times \mathrm{Breadth}$
= JH$\times$HG
= (2$\times$4) cm²
= 8 cm²
Area of the figure = Area of rectangle ABFK + Area of rectangle MLKG + Area of rectangle JHGF + Area of square BCDE
= (9 + 5 + 6 + 8) cm²
= 28 cm²

(ii) Area of rectangle CEFG= $\mathrm{Length}\times \mathrm{Breadth}$
= EF$\times$CE
= (1$\times$5) cm² (CE = EA − AC)
= 5 cm²
Area of rectangle ABDC = $\mathrm{Length}\times \mathrm{Breadth}$
= AB$\times$BD
= (1$\times$2) cm²
= 2 cm²

Area of rectangle HIJG = $\mathrm{Length}\times \mathrm{Breadth}$
= HI $\times$ IJ
= (1$\times$2) cm²
= 2 cm²
Area of the figure = Area of rectangle CEFG + Area of rectangle HIJG + Area of rectangle ABDC
= (5+2+2) cm²
= 9 cm²

(iii) In the figure, there are 5 squares, each of whose sides are 6 cm in length.
Area of the figure = 5 $\times$ Area of square
= 5$\times$(side)²
= 5$\times$(6)² cm²
= 180 cm²