Question

FIND THE AREA OF A TRAPEZIUM WHOSE PARALLEL SIDE ARE 25CM, 13CM AND OTHER SIDES ARE 15 CM AND 15CM?????

Answer 1

Answer:

The area of trapezium is 261.25 cm².

Step-by-step-explanation:

In figure, we have given that,

AD = 13 cm.

BC = 25 cm.

AB = CD = 15 cm.

Construction:

Draw AE ⊥ seg BC, DF ⊥ seg BC.

Now,

In figure, in ⎕ AEFD, ∠ AEF = ∠ DFE = 90°.

∴ ⎕ AEFD is rectangle. [ By definition ]

∴ AD = EF = 13 cm. - - ( 1 )

[ Opposite sides of rectangle are congruent. ]

Now,

In Δ AEB & Δ DFC,

AB = CD - - - [ Given ]

∠ AEB = ∠ DFC - - - [ Each of 90°. ]

AE = DF - - - [ Perpendiculars between two segments are congruent. ]

∴ Δ AEB ≅ Δ DFC - - - [ Hypotenuse side test ]

∴ BE = CF - - - [ c. s. c. t. ]

Now,

BC = BE + EF + FC

→ 25 = x + 13 + x - - - [ From ( 1 ) ]

→ 25 = 2x + 13

→ 25 - 13 = 2x

→ 2x = 12

→ x = 12 /2

→ x = 6 cm.

∴ BE = CF = 6 cm.

Now,

In Δ AEB, ∠ AEB = 90°.

∴ By Pythagoras theorem,

( AB )² = ( BE )² + ( AE )²

→ ( 15 )² = 6² + ( AE)²

→ 225 = 36 + ( AE )²

→ 225 - 36 = ( AE )²

→ 189 = ( AE )²

∴ AE = 13.747 - - - [ Taking square roots ]

∴ AE ≈ 13.75 cm.

Now,

A ( ⎕ ABCD ) = 1 / 2 × ( AD + BC ) × AE

→ A ( ⎕ ABCD ) = 1 / 2 × ( 13 + 25 ) × 13.75

→ A ( ⎕ ABCD ) = 1 / 2 × ( 38 ) × 13.75

→ A ( ⎕ ABCD ) = 1 / 2 × 38 × 13.75

→ A ( ⎕ ABCD ) = 1 / 2 × 522.5

→ A ( ⎕ ABCD ) = 261.25 cm².

∴ The area of trapezium is 261.25 cm².