Question

The figure, given below, shows a trapezium ABCD. M and N are the mid-point of the non-parallel sides AD and BC respectively. Find: 

1. MN, if AB = 11 cm and DC = 8 cm.
2. AB, if DC = 20 cm and MN = 27 cm.
3. DC, if MN = 15 cm and AB = 23 cm.

Answer 1

Let we draw a diagonal AC as shown in the figure below,

(i) Given that AB = 11 cm, CD = 8 cm

From triangle ABC

ON = `[1]/[2]` AB

= `[1]/[2]` × 11

= 5.5 cm

From triangle ACD

OM = `[1]/[2]` CD

=`[1]/[2]` × 8

= 4 cm

Hence, MN = OM + ON

= (4 + 5.5)

= 9.5 cm

(ii) Given that CD = 20 cm, MN = 27 cm

From triangle ACD

OM = `[1]/[2]` CD

= `[1]/[2]` × 20

= 10 cm

Therefore, ON = 27 - 10 = 17 cm

From triangle ABC

AB = 2ON

= 2 × 17

= 34 cm

(iii) Given that AB = 23 cm, MN = 15 cm

From triangle ABC

ON =`[1]/[2]` AB

=`[1]/[2]` × 23

= 11.5 cm

OM = 15 - 11.5

OM = 3.5 cm

From triangle ACD

CD = 2OM

= 2 × 3.5

CD = 7 cm