Question

Calculate the area of the shaded region in each of the figures given below.
Fig. (ii) has uniform width of 3 cm and it is given that AB = CD.

Answer 1

(i) Complete the rectangle as shown below:

Area of the shaded region = [Area of rectangle ABCD - Area of rectangle EFGD] sq. units
= [(AB $\times$ BC) - (DG $\times$ GF)] m²
= [(24 m $\times$ 19 m) - {(24 - 4) m $\times$ 16.5 m} ]
= [(24 m $\times$ 19 m) - (20 m $\times$ 16.5) m]
= (456 - 330) m² = 126 m²

(ii) Complete the rectangle by drawing lines as shown below:

Area of the shaded region ={(12 $\times$ 3) + (12 $\times$ 3) + (5$\times$ 3) + {(15 - 3 - 3) $\times$3)} cm²
= { 36 + 36 + 15 + 27} cm²
= 114 cm²