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