Question

Two parallel sides of a trapezium are 60 m and 77 m and the other sides are 25 m and 26 m. Find the area of the trapezium.

Answer 1

Given: AB = 77 m , CD = 60 m, BC = 26 m and AD = 25m 

AE and CF are diagonals.

DE and CF are two perpendiculars on AB. 

Therefore, we get, DC = EF = 60 m 

Let’s say, AE = x 

Then BF = 77 – (60 + x) 

BF = 17 – x …(1) 

In right △ADE, 

From Pythagoras theorem, 

DE² = AD² − AE² 

DE² = 25² − x² ….(2) 

In right △BCF 

From Pythagoras theorem, 

CF² = BC² − BF² 

CF² = 26² − (17−x)² [Uisng (1)] 

Here, DE = CF 

So, DE² = CF² 

⇒ 25² − x² = 26² − (17−x)² 

625 − x² = 676 – (289 −34x + x²) 

625 − x² = 676 – 289 + 34x – x² 

238 = 34x 

x = 7 

⇒ DE² = 25² – (7)² 

DE² = 625 − 49 

DE = 24 

Area of trapezium = 1/2 x (60 + 77) x 24 

= 1644 

Area of trapezium is 1644 m²