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
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: