Question

ABCD is a trapezium where AB║DC. AB = 78 cm , CD = 52cm , AD = 28cm and BC = 30 cm. Find the area of trapezium without using herons formula

Answer 1

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