BC = CD. So BC and CD are half of BD

= 12cm ÷ 2
= 6cm

GF = 10cm - 8cm = 2cm
AG = BC = 6cm

Rectangle ABCG = 10cm x 6cm = 60cm²
Rectangle CDEF = 8cm x 6cm = 48cm²

Triangle AGF = ½ x 2cm x 6cm = 6cm²
Triangle ABD = ½ x 10cm x 12cm = 60cm²
Triangle FED = ½ x 6cm x 8cm = 24cm²

Triangle ADF

= Area of two rectangles - area of the three triangles

= 60 cm² + 48cm² - 6cm² - 60cm² - 24cm²
= 18cm²




Alternatively,


Extend AG and ED to meet each other. You'll get a big rectangle.


Now triangle ABD is half of this rectangle.

The other half is also a triangle with the same area. It includes the two small triangles FED, AGF and a small rectangle with length 6cm and width 2cm.

Area of small triangle
= 6cm x 2cm = 12cm²

Triangle ADF
= Big triangle identical to ABD - small rectangle - triangle FED - triangle AGF

= 60cm² - 12cm² - 6cm² - 24cm²
= 18cm²