31. ABCD has area equal to 28 sq. unit. BC is parallel to AD and BA perpendicular to AD. If BC = 6 and AD = 8,

then value of CD =

B. 213

A. 2 12

C. 4

D. 275

The value of CD is 2√5

Step-by-step explanation:

* Lets describe the figure to know its name

- ABCD is a quadrilateral

∵ BC parallel to AD

∵ BC = 6 units and AD = 8 units

- The quadrilateral which has two parallel sides not equal in length is a

trapezoid

∴ ABCD is a trapezoid, where BC and AD are its bases

∵ BA perpendicular to AD

∴ BA is the height of the trapezoid

- The area of the trapezoid = 1/2 (base 1 + base 2) * its height

∵ The bases of the trapezoid are BC and AD

∵ BC = 6 and AD = 8

∵ Its area = 28 units²

∴ 1/2 (6 + 8) * height = 28

∴ 1/2 (14) * height = 28

∴ 7 * height = 28 ⇒ divide both sides by 7

∴ height = 4

∵ The height is BA

∴ BA = 4 unit

- To find the length of CD draw a perpendicular line from C to AD and

meet it at E

∵ BA and CE are perpendicular to AD

∴ BA / / CE

∵ BC / / AD

- Perpendicular lines between parallel lines are equal in lengths

∴ BA = CE and BC = AE

∵ BA = 4 and BC = 6

∴ CE = 4 and AE = 6

∵ AD = 8 units

∵ AD = AE + ED

∴ 8 = 6 + ED ⇒ subtract 6 from both sides

∴ ED = 2 units

- In ΔCED

∵ m∠CED = 90°

∴ CD = √[ (CE) ² + (ED) ²] ⇒ Pythagoras theorem

∵ CE = 4 and ED = 2

∴ CD = √[ (4) ² + (2) ²] = √[16 + 4] = √20 = 2√5

* The value of CD is 2√5