Question

the non parallel sides of trap. are equal and measure 10cm. if the parallel sides measure 13cm and 25cm. find the area pf trap
pls tell in simple way​

Answer 1

GiveN :

• The non parallel sides of trap. are equal and measure 10cm. The parallel sides measure 13cm and 25cm.

To FinD :

• Find the area of trapezium.

SolutioN :

In isosceles ABCD trapezium,

AB = EF = 13 cm.

Let the distance between parallel sides be 'h'

And, CE = FD = a cm

In parallel side CD :

⇒ CD = CE + EF + FD

⇒ 25 = a + 13 + a

⇒ 25 - 13 = 2a

⇒ 12 = 2a

⇒ a = 12/2

⇒ a = 6 cm

ΔACE and ΔBDF are equilateral and right angled triangles where, AC = BD = 10 cm and CE = DF = a cm = 6 cm, AE = BF = h cm.

Using pythagoras theorem in ΔACE

⇒ AC² = CE² + AE²

⇒ 10² = 6² + h²

⇒ 100 - 36 = h²

⇒ h² = 64

⇒ h = √64

⇒ h = 8 cm.

∴ Distance between parallel sides are = 8 cm.

Now,

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

⇒ 1/2 (13 + 25) × 8

⇒ 38 × 4

⇒ 152

∴ Area of trapezium = 152 cm²