Question :-Two parallel SIDES of a trapezium and the distance between them are in the ratio 4:3:2 if the area of the trapezium is 1372cm² then find the parallel sides and HEIGHT.Given :-Two parallel sides of a trapezium and the distance between them are in the ratio 4:3:2.Area of the Trapezium is 1372cm²To Find :-The Measures of Two parallel sides and Height .Solution :-Let the First Parallel Side be 4xLet the Second Parallel Side be 3xLet the Height of the PARALLELOGRAM be 2x ★ According to the Question ★⇒ Area of Trapezium = ½ × height × SUM of parallel sides ⇒ 1372 = ½ × 2x × ( 4x + 3x )⇒ 1372 = ½ × 2x × 7x⇒ 1372 = ½ × 14x²⇒ 1372 = 7x²⇒ 1372/7 = x²⇒ 196 = x²⇒ √196 = x⇒ 14 = x________________★Measures of Sides and Height★⇒First Parallel side 4x = 4 × 14 = 56cm⇒2nd Parallel side 3x = 3 × 14 = 42cm⇒Height = 2x = 2 × 14 = 28cm________________Verification :-⇒ Area of Trapezium = ½ × height × sum of parallel sides ⇒ 1372 = ½ × 28 × ( 56 + 42 )⇒ 1372 = 14 × 98⇒ 1372 = 1372Hence, Verified________________