The cross-section of a piece of metal 2 m in length is shown in the adjoining figure. Calculate :

(i) the area of its cross-section;

(ii) the volume of piece of metal;

(iii) the weight of piece of metal to the nearest kg, if 1 cm³ of the metal weighs 6.5 g.

Given,

Length of the metal piece = 2 m = 200 cm.

(i) From figure,

Rectangle ABCD :

Length (AB = CD) = 12 cm

Breadth (BC = AD) = 13 cm.

Area of rectangle ABCD = length × breadth

= 12 × 13 = 156 cm².

Triangle DEF :

Height (DF) = DC - FC = 12 - 8 = 4 cm.

Base (DE) = AE - AD = 16 - 13 = 3 cm.

Area of triangle DEF = $\dfrac{1}{2}$ × Base × Height

= $\dfrac{1}{2}$ × 3 × 4

= 6 cm².

Total cross-section area = 156 + 6 = 162 cm².

Hence, area of cross-section = 162 cm².

(ii) Calculating the volume of metal piece,

Volume of metal piece = Area of cross section × Length

= 162 × 200

= 32400 cm³.

Hence, volume of metal piece = 32400 cm³.

(iii) Given,

1 cm³ of metal = 6.5 g.

Calculating the weight of the metal piece,

Total weight of the metal piece = Volume × Weight of metal at 1 cm³

= 32400 × 6.5

= 210600 g.

1000 g = 1 kg

∴ 210600 g = $\dfrac{210600}{1000}$ kg

= 210.6 kg ≈ 211 kg.

Hence, weight of the piece of the metal = 211 kg.