Math, asked by adiyachoudhary, 4 months ago

9. In Fig. 12.8. ABCD is a trapezium in which
AB II CD and CE L AB. Also AB = 10 cm,
CD = 6 cm and BC = 5 cm. Find the area of
the trapezium​

Answers

Answered by sahananeel07
2

Answer:Draw CE ∥ AD and CF ⊥ AB.  

Now, EB = (AB - AE) = (AB - DC) = (78 - 52) cm = 26 cm,  

CE = AD = 28 cm and BC = 30 cm.  

Now, in ∆CEB, we have  

S = ¹/₂ (28 + 26 + 30) cm = 42 cm.  

(s - a) = (42 - 28) cm = 14 cm,  

(s - b) = (42 - 26) cm = 16 cm, and  

(s - c) = (42 - 30) cm = 12 cm.  

area of ∆CEB = √{s(s - a)(s - b)(s - c)}  

                     = √(42 × 14 × 16 × 12) cm²  

                     = 336 cm²

Also, area of ∆CEB = ¹/₂ × EB × CF  

                              = (¹/₂ × 26 × CF) cm²  

                              = (13 × CF) cm²

Therefore, 13 × CF = 336  

⇒ CF = 336/13 cm

Area of a trapezium ABCD

= {¹/₂ × (AB + CD) × CF} square units  

                   = {¹/₂ × (78 + 52) × ³³⁶/₁₃} cm²

                   = 1680 cm²

Step-by-step explanation:

Similar questions