Question

Calculate the area of each one of the shaded regions given below:
Figure

Answer 1

(i) Area of rectangle ABDC = Length $\times$ Breadth
= AB$\times$AC (AC = AE − CE)
= $\left(1\times 8\right){\mathrm{m}}^2$
= 8 m²
Area of rectangle CEFG = Length $\times$ Breadth
= CG$\times$GF (CG = GD + CD)
= $\left(9\times 2\right){\mathrm{m}}^2$
= 18 m²
Area of the complete figure = Area of rectangle ABDC + Area of rectangle CEFG
= (8 + 18) m²
= 26 m²


(ii) Area of rectangle AEDC = Length $\times$ Breadth
= ED $\times$ CD
= $\left(12\times 2\right){\mathrm{m}}^2$
= 24 cm²
Area of rectangle FJIH = Length $\times$ Breadth
= HI $\times$ IJ
= $\left(1\times 9\right){\mathrm{m}}^2$
= 9 m²
Area of rectangle ABGF = Length $\times$ Breadth
= AB $\times$ AF {(AB = FJ − GJ) and AF = EH − (EA + FH)}
= $\left(7\times 1.5\right){\mathrm{m}}^2$
= 10.5 m²

Area of the complete figure = Area of rectangle AEDC + Area of rectangle FJIH + Area of rectangle ABGF
= (24 + 9 + 10.5) m²
= 43.5 m²



(iii) Area of the shaded portion = Area of the complete figure − Area of the unshaded figure
= Area of rectangle ABCD − Area of rectangle GBFE
=(CD$\times$AD) − (GB$\times$BF)
=$\left\{(12\times 9)-(7.5\times 10)\right\}{\mathrm{m}}^2$ (BF = BC − FC)
=(108 − 75) m²

=33 m²