Question

In the adjoining figure, DC || AB. BC = 8 cm, AD = 17 cm, CD = 24 cm.

Find

1. AB 
2. Area of trapezium ABCD

Answer 1

Given:

DC || AB, BC = 8 cm, AD = 17 cm, CD = 24 cm.

Step-wise calculation:

1. Put A at (0, 0) and AB = x so B is (x, 0).

Then C is (x, 8) and D is (x – 24, 8).

2. Use Pythagoras on AD: 

Distance AD²

= (x – 24)² + 8²

= 17²

3. Compute: 

(x – 24)² + 64 = 289

(x – 24)² = 225

x – 24 = ±15

⇒ x = 24 ± 15

⇒ x = 39 or x = 9

4. From the figure, 

D lies to the left of A.

So, x = 9 cm the other root would place D to the right of A.

5. Area of trapezium 

= `1/2 xx "Sum of parallel sides" xx "Distance between them"` 

= `1/2 xx (AB + CD) xx BC`

Using AB = 9, CD = 24, BC = 8 gives:

Area = `1/2 xx (9 + 24) xx 8`

= `1/2 xx 33 xx 8`

= 132 cm²

AB = 9 cm.

Area (ABCD) = 132 cm².