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Answer :

We can observe, Area of the octagonal surface= area of trapezium ABCH + area of rectangle HCDG + area of trapezium GDEF

Finding area of different parts:

Area of trapezium ABCH = Area of trapezium GDEF

\(=\frac { 1 }{ 2 }\times (a + b) \times h\)

\(=\frac { 1 }{ 2 }\times (11 + 5) \times 4\)

\(=\frac { 1 }{ 2 }\times 16 \times 4\)

\(= 32 m^2\)

Area of rectangle HCDG =\( l \times b = 11 m \times 5 m = 55 m^2\)

Area of the octagonal surface = \(32 m^2 + 55 m^2 + 32 m^2 = 119 m^2\)

Hence, the required area = \(119 m^2\).

- 1.The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.
- 2.The area of a trapezium is \(34 cm^2\) and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.
- 3.Length of the fence of a trapezium A shaped field ABCD is 120 m. IF BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
- 4.The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
- 5.The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
- 6.Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
- 7.The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per \(m^2\) is ₹ 4.
- 8.Mohan wants to buy a trapezium shaped field. Its side along the. river is parallel to and twice the side along the road. If the area of this field is 10500 \(m^2\) and the perpendicular distance between the two parallel sides is 100m, find the length of the side along the river.
- 10.There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways. Find the area of this park using both ways. Can you suggest some other way of finding its area?
- 11.Diagram of the picture frame has outer dimensions = \(24 cm \times 28 cm\) and inner dimensions \(16 cm \times 20 cm\). Find the area of each section of the frame, if the width of each section is the same.

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