Parallel sides of trapezium = 4.6 cm & 8 cmDistance between them = 2.5 cmBase of triangle = 1.7 cmHeight of triangle = 1.4 cmTo Find :The area of the shaded region. SOLUTION :Analysis :Here the formula of area of trapezium and triangle is used. First we have to SEPARATELY find the area of both trapezium and triangle. Then subtracting the area of trapezium from area of triangle we will be getting the area of the shaded region. Required Formula :Area of trapezium = ½ × (a + b) × dArea of triangle = ½ × BASE × heightwhere, (a + b) = sum of parallel sidesd = distance between themExplanation :Area of trapezium :We know that if are given TWO parallel sides and the distance between them then our required formula is, Area of trapezium = ½ × (a + b) × dwhere, a = 4.6 cmb = 8 cmd = 2.5 cmUsing the required formula and substituting the required values, ⇒ Area of trapezium = ½ × (a + b) × d⇒ Area of trapezium = ½ × (4.6 + 8) × 2.5⇒ Area of trapezium = ½ × 12.6 × 2.5⇒ Area of trapezium = 1 × 6.3 × 2.5⇒ Area of trapezium = 15.75 ∴ Area of trapezium = 15.75 cm².Area of triangle :We know that if are given the base and the height then our required formula is, Area of triangle = ½ × base × heightwhere, Base = 1.7 cmHeight = 1.4 cmUsing the required formula and substituting the required values, ⇒ Area of triangle = ½ × base × height⇒ Area of triangle = ½ × 1.7 × 1.4⇒ Area of triangle = 1 × 1.7 × 0.7 ⇒ Area of triangle = 1.19∴ Area of triangle = 1.19 cm².Area of shaded region :Area of shaded region = area of trapezium - area of trianglewhere, Area of trapezium = 15.75 cm².Area of triangle = 1.19 cm².Using the required formula and substituting the required values, ⇒ Area of shaded region = area of trapezium - area of triangle⇒ Area of shaded region = 15.75 - 1.19 ⇒ Area of shaded region = 14.56∴ Area of shaded region = 14.56 cm².Area of shaded region is 14.56 cm².