33 (a)  The figure (i) given below is a trapezium.  Find the length of BC and the area of the trapezium.  Assume AB = 5 cm, AD = 4 cm, CD = 8 cm.

const a line BE perpendicular to CD & AB.
BE=4cm
CE=CD-DE
CE=8cm-5cm=3cm
BC²=CE²+BE²
BC²=9+16
BC²=25
BC=5cm
Area of trapezium ABCD=1/2*(sum of parallel sides)*distance between the parallel sides
Area of trapezium ABCD=1/2*(5+8)*4
Area of trapezium ABCD=13*2
Area of trapezium ABCD=26cm^​2


Therefore, area of the trapezium is 26sqcm and measure of its side BC is 5cm.