Question

Find the area of a trapezium whose parallel sides are AB = 12 cm, CD = 36 cm and the non-parallel sides are BC = 15 cm and AG = 15 cm. 

Answer 1

In trapezium ABCD, draw CE ∥ DA. 

Now CE = 15 cm 

Since, DC = 12 cm so, AE = 12 cm 

Also, EB = AB - AE = 36 - 12 = 24 cm 

Now, in ∆ EBC 

S = (15 + 15 + 24)/2 

= 54/2 

= 27 

= √(27 × 12 × 12 × 3) 

= √(3 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 3 × 3) 

= 3 × 3 × 3 × 2 × 2

= 108 cm²

Draw CP ⊥ EB. 

Area of ∆EBC = 1/2 × EB × CP 

108 = 1/2 × 24 × CP

108/12 = CP 

⇒ CP = 9 cm Therefore, h = 9 cm

Now, area of triangle = √(s(s - a) (s - b) (s - c)) 

= √(27 (27 - 15) (27 - 15 ) (27 - 24)) 

Now, area of trapezium = 1/2(p₁ + p₂) × h

= 1/2 × 48 × 9

= 216 cm²

Answer 2

⭐ Here is your answer mate ⭐

❄ Hope this attached file helped you ❄