Question

Two parallel sides DC and AB of a Trapezium are 12 cm and 36 cm respectively. If non parallel sides are each equal to 15 cm find the area of a Trapezium

Answer 1

Answer:

Calculation:

Step-by-step explanation:

Draw CF and DE perpendicular on AB

AS, DC is parallel to AB and and DE is parallel to CF

⇒ DCEF is a parallelogram

Also, ∠DEF = ∠CFE = 90°

⇒ DCEF is a rectangle

⇒ EF = 12 cm

⇒ AE + EF + FB = 36 cm

⇒ AE + 12 + FB = 36 cm

⇒ AE + FB = 24 cm

⇒ 2 × AE = 24 (AE = AF)

⇒ AE = 12 cm

⇒ FB = 12 cm

In ΔDEA, By using pythagoras theorem

⇒ DA2 = DE2 + AE2

⇒ 152 = DE2 + 122

⇒ DE2 = 225 - 144

⇒ DE2 = 81

⇒ DE = 9 cm = Height of trapezium

⇒ Area of trapezium = 1/2 × (Sum of parallel sides) × Height

⇒ Area of trapezium = 1/2 × (12 + 36) × 9

∴ Area of trapezium = 216 cm2