Question

two parallel sides of a trapezium are 60cm and 77cm and other sides are 25cm and 26cm find the area of trapezium.

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Answer 1

Area of trapezium = 1/2 × sum of parallel sides × height

Answer 2

Answer:

1644 cm²

Step-by-step explanation:

Let ABCD be the trapezium in which AB || CD and BF ⊥ DC.

∴ AE = BF and AB = EF = 60 cm.

Let DE = 'x' cm and FC = 77 - (60 + x) = 17 - x.

(i) In ΔAED:

AE² = AD² - DE²

      = 625 - x²

(ii) In ΔBFC,

BF² = (BC)² - (FC)²

      = (26)² - (17 - x)²

      = 676 - (289 + x² - 34x)

      = 676 - 289 - x² + 34x

      = 387 - x² + 34x

But AE = BF

On Squaring both sides, we get

⇒ AE² = BF²

⇒ 625 - x² = 387 - x² + 34x

⇒ 625 - x² - 387 + x² - 34x = 0

⇒ 238 - 34x

⇒ x = 7.

∴ AE = √625 - 49

        = √576

        = 24 cm

∴ Area of trapezium ABCD = (1/2) * AE * (AB + CD)

                                            = (1/2) * 24 * (60 + 77)

                                           = 1644 cm²

Therefore, Area of trapezium = 1644 cm².

Hope it helps!