Question

the parallel sides of a trapezium are 25 cm and 13 cm . The length of each non-parallel side is 10cm . Find the area of the trapezium ​

Answer 1

Step-by-step explanation:

25x13

325

325-10

315 ans

Answer 2

Let ABCD is a trapezium, AB || DC,

AB = 25, CD = 11 , AD= 13 , BC =1cm

Draw CL || AB and CM || DA meeting AB at L and M respectively.

Therefore, AMCD is a parallelogram.

MC = AD = 13cm AM = DC =11cm

MB = (AB—AM) = (25—11) = 14 cm

In triangle CMB, CM = 13 , MB = 14 , BC = 15

let ML = x, CL = y cm, LB = 14 – x ,

In triangle CML,

CL²= CM² – ML²

y² = 13² – x²...............(1)

In triangle CLB,

CL² = CB² – LB²

y² = 15² – (14—x)²............... (2)

From (1) and (2)

13² – x² = 15² – (14—x)²

169 – x² = 225 – (196 + x²– 28x)

169 – x² = 225 – 196 – x² + 28x

28x = 169 + 196 – 225 + x² – x²

28x = 140

X = 5 cm

Substitute x value in eq (1)

y² = 13² – x²

y² = 13² – 5²

y² = 169 – 25

y² = 144

y = 12 cm

Therefore, CL = 12 cm that is height of the trapezium = 12 cm

Area of trapezium =1/2×(sum of parallel sides)×height

Area of trapezium =1/2× (25 + 11) × 12 = 216 cm²