Question

Please solve tye answer step by step​

Answer 1

Answer:

(a) 28cm

Step-by-step explanation:

The area of a trapezium = 1/2(Sum of parallels)(height)

36 = 1/2(12+6)(h)

h = (36*2)/(12+6)

h = 72/18

h = 4 cm

Now, in ∆AFB and ∆DCE,

FB = EC

AF = DE

Angle(FBA) = Angle(ECD) = 90°

Thus, by SAS congruency criterion, ∆AFB≈∆DCE.

That is, AB = CD.

Also, AD= 12cm

AB + BC + CD = 12cm

2AB + 6 = 12cm

AB = 3 cm

Use Pythagorean theorem in ∆ABF,

AB² + FB² = AF²

AF² = 3² + 4²

AF² = 9+16

AF = 5 cm

Since, the trapezium is isosceles, the slant sides of the trapezium are equal. That is, AF = DE = 5cm.

Now, the perimeter of the trapezium = AF + FE + ED + DC + CB + BA = 5+6+5+3+6+3 cm = 28cm