the length of the parallel sides of an isosceles trapezium are 10 cm and 18 cm and the length of each of the non parallel side is 5 cm find the area of the trapezium
Answers
Answer:
Given:
The parallel sides of a trapezium are 10 cm and 18 cm
Each non parallel side is 8 cm
Formula used:
Area of trapezium = 1/2 × (Sum of parallel sides) × Height
Calculation:
F1 Suhani Ravi 28.07.21 D1
Draw CF and DE perpendicular on AB
AS, DC is parallel to AB and and DE is parallel to CF
⇒ DCEF is a parallelogram
Also, ∠DEF = ∠CFE = 90°
⇒ DCEF is a rectangle
⇒ EF = 12 cm
⇒ AE + EF + FB = 18 cm
⇒ AE + 10 + FB = 18 cm
⇒ AE + FB = 8 cm
⇒ 2 × AE = 8 (AE = AF)
⇒ AE = 4 cm
⇒ FB = 4 cm
In ΔDEA, By using pythagoras theorem
⇒ DA2 = DE2 + AE2
⇒ 82 = DE2 + 42
⇒ DE2 = 64 - 16
⇒ DE2 = 48
⇒ DE = 4√3 cm = Height of trapezium
⇒ Area of trapezium = 1/2 × (Sum of parallel sides) × Height
⇒ Area of trapezium = 1/2 × (10 + 18) × 4√3 = 96.88 = (97 cm2 nearest)
∴ Area of trapezium is 97 cm2