Question

In Fig, a parallelogram is drawn in a trapezium, the area of the parallelogram is 80 cm2, find the area of the trapezium.

Answer 1

In ΔCEF,

CE = 10 cm and EF = 6cm

Using Pythagoras theorem:

CE2 = CF2 + EF2

CF2 = CE2 – EF2

CF2 = 102 – 62

CF2 = 100-36

CF2 = 64

CF = 8 cm

Area of parallelogram = 80 cm2

From the figure we can write,

Area of trapezium = Area of parallelogram AECD + Area of area of triangle CEF

Area of trapezium = base × height + 1/2 (base × height)

Area of trapezium = 10 × 8 + 1/2 (12 × 8)

Area of trapezium = 80 + 48 = 128

∴ Area of trapezium = 128 cm2