The adjoining figure shows the cross-section of a concrete wall to be constructed. It is 1.9 m wide at the bottom, 90 cm wide at the top and 5 m high. If its length is 20 m, find :

(i) the cross-sectional area;

(ii) the volume of the concrete in the wall.

Let the bottom width be 'a' and top width be 'b'.

Given,

Bottom width (a) = 1.9 m

Top width (b) = 90 cm = 0.9 m

Height (h) = 5 m

Length = 20 m

(i) Cross-sectional area :

$\text{Area of trapezium} = \dfrac{1}{2} \times \text{ (sum of // sides)} \times \text{ (distance between them)} \\[1em] = \dfrac{1}{2} \times (1.9 + 0.9) \times 5 \\[1em] = \dfrac{1}{2} \times 2.8 \times 5 \\[1em] = 1.4 \times 5 \\[1em] = 7 \text{ m}^2.$

Hence, area of cross-section = 7 m².

(ii) Volume of concrete :

Volume of concrete = Area of cross-section × Length of the wall.

= 7 × 20

= 140 m³.

Hence, volume of concrete = 140 m³.