Question

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 sides is 5 cm find the area of the trapezium​

Answer 1

Answer:

So we can use Pythagoras Theorem to find the missing side. Answer: The height is 97 cm ²

Step-by-step explanation:

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