In figure given below, AB || DC, BC = AD = 13 cm, AB = 22 cm and DC = 12 cm. Calculate the height of the trapezium ABCD.

From figure,

EF = DC = 12 cm

Since,

AD = BC and DE = CF = h (height)

∴ AE = FB = x.

⇒ AB = AE + EF + FB

⇒ 22 = x + 12 + x

⇒ 2x = 22 - 12

⇒ 2x = 10

⇒ x = 5 cm.

In right triangle ADE,

By pythagoras theorem,

⇒ AD² = DE² + AE²

⇒ 13² = h² + 5²

⇒ 169 - 25 = h²

⇒ h² = 144

⇒ h = 12 cm.

Hence, height = 12 cm.