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.213A. 2 12C.4D. 275

Answer:The value of CD is 2√5Step-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