Find the area of shaded regions : Example 1 : Solution : Area of shaded region = Area of large rectangle – Area of small rectangle Area of rectangle = Length ⋅ width Large rectangle : Length = 12 cm width = 9 cm Area of large rectangle = (12 ⋅ 9) = 108 cm2------(1) Small rectangle : Length = 6 cm width = 3 cm Area of small rectangle = (6 ⋅ 3) = 18 cm2------(2) (1) – (2) = (108 – 18) cm2 = 90 cm2 So, area of shaded region is 90 cm2 Example 2 : Solution : Area of shaded region = Area of rectangle – 2(Area of triangle) Area of rectangle = length ⋅ width Area of triangle = (1/2) ⋅ base ⋅ height Area of rectangle : Area of rectangle = (9 ⋅ 5) = 45 m2------(1) 2(Area of triangle) : base = 4 m height = 3 m 2(Area of triangle) = 2(1/2) ⋅ 4 ⋅ 3 = 2(6) = 12 m2------(2) (1) – (2) Area of shaded region = (45 – 12) m2 = 33 m2 So, area of shaded region is 33 m2 Example 3 : Solution : Area of shaded region = Area of rectangle + Area of square Area of rectangle : Length = (4 + 3) km ==> 7 km Width = 3 km Area of rectangle = (7 ⋅ 3) = 21 km2-----(1) Area of square : side = 3 km Area of square = (side)2 = (3)2 = 9 km2-----(2) (1) + (2) = (21 + 9) km2 Area of shaded region = 30 km2 So, area of shaded region is 30 km2 Example 4 : Solution : Area of shaded region = Area of triangle + Area of rectangle Area of triangle : Area of triangle = (1/2) ⋅ base ⋅ height base = 6 cm and height = 2 cm Area of triangle = (1/2 ⋅ 6 ⋅ 2) = 6 cm2-----(1) Area of rectangle : Area of rectangle = Length . width Length = 6 cm and Width = 3 cm Area of rectangle = (6 ⋅ 3) = 18 cm2-----(2) (1) + (2) Area of shaded region = (6 + 18) cm2 = 24 cm2 So, area of shaded region is 24 cm2 Example 5 : Solution : Area of shaded region = Area of large rectangle – Area of small rectangle Area of rectangle = Length ⋅ width Large rectangle : Length = 17 m and width = 10 m Area of large rectangle = (17 ⋅ 10) = 170 m2------(1) Small rectangle : Length = (17–2) ==> 15 m width = (10–2) ==> 8 m Area of small rectangle = (15 ⋅ 8) = 120 m2------(2) (1) – (2) = (170 – 120) m2 = 50 m2 So, area of shaded region is 50 m2 Example 6 : Solution : Area of shaded region = Area of rectangle – Area of parallelogram Area of parallelogram = base ⋅ height Area of rectangle : Area of rectangle = Length ⋅ width Length = 13 cm and width = 8 cm Area of rectangle = (13 ⋅ 8) = 104 cm2-----(1) Area of parallelogram : base = 9 cm and height = 7 cm Area of parallelogram = (9 ⋅ 7) = 63 cm2------(2) (1) – (2) = (104 – 63) cm2 Area of shaded region = 41 cm2 So, area of shaded region is 41 cm2 Example 7 : Solution : Area of shaded region = Area of large parallelogram – Area of small parallelogram Large
parallelogram : base = 10.2 m and height = 7.8 m Area of large parallelogram = (10.2 × 7.8) = 79.56 m2------(1) Small parallelogram : base = 7.2 m and height = 4.8 m Area of small parallelogram = (7.2 × 4.8) = 34.56 m2------(2) (1) – (2) = (79.56 – 34.56) m2 = 45 m2 So, area of shaded region is 45 m2 Example 8 : A rectangular lawn 18 m by 30 m is surrounded by a concrete path 1 m wide. Draw a diagram of the situation and find the total area of concrete. Solution : Area of shaded region = Area of rectangular concrete path – Area of rectangular lawn Area of rectangle = Length . width Area of rectangular concrete path : Length = (30+2) m ==> 32 m width = (18+2) m ==> 20 m Area of rectangular concrete path = (32 . 20) = 640 m2------(1) Area of rectangular lawn : Length = 30 m and width = 18 m Area of rectangular lawn = (30 . 18) = 540 m2------(2) (1) – (2) = (640 – 540) m2 = 100 m2 So, total area of concrete is 100 m2 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. Kindly mail your feedback to We always appreciate your feedback. ©All rights reserved. onlinemath4all.com |