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

20

step-by-step explanation: