Question

in the adjoining figure ABCD is trapezium AB//CD and its area is 33cm2 . From the information given in the figure find the length of all the sides

Answer 1

Given: AB∥CD

Area of a trapezium =

2

1

× (sum of parallel sides) × (height)

=

2

1

×(x+2x+1)(x−4)

=

2

1

(3x+1)(x−4)

=

2

3x

2

−12x+x−4

=

2

3x

2

−11x−4

Given: the area of trapezium is 33 cm

2

⇒

2

3x

2

−11x−4

=33

⇒3x

2

−11x−4=66

⇒3x

2

−11x−70=0

⇒3x

2

−21x+10x−70=0

⇒3x(x−7)+10(x−7)=0

⇒(3x+10)(x−7)=0

∴ x=7 units

Hence the sides of the trapezium are:

∣AB∣=x=7 cm

∣BC∣=x−2=5 cm

∣CD∣=2x+1=11 cm

∣AD∣=∣BC∣=5 cm