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Short Answer Type

21.

Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 cm, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

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22.

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.

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23.

The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.

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24. 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.

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Long Answer Type

25. 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 m² is Rs 4.

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26.

Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along road. If the area of his field is 10500 m² and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

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27.

Top surface of a raised platform is in the shape of regular octagon as shown in the figure. Find the area of the octagonal surface.

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28. 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?

Jyoti’s diagram:
The given shape is splitted into two congruent trapeziums.
Area of one trapezium = $1 half cross times left square bracket 15 plus 30 right square bracket space cross times space 15 over 2 space straight m squared$

= $1 half cross times 45 cross times 15 over 2 straight m squared$

= $675 over 4 straight m squared$

∴ Area of the pentagonal shape = $2 cross times 675 over 4 straight m squared space equals space 675 over 2 space straight m squared space equals space 337.5 space straight m squared$
Kavita's diagram:
The given shape is splitted into a square and a triangle.
Area of the square = $space space 15 space straight m space cross times space 15 space straight m space equals space 225 space straight m squared$

Area of the triangle = $1 half cross times 15 cross times 15 space equals space 225 over 2 space straight m squared space equals space 112.5 space straight m squared$

∴ Area of the pentagonal shape = $112.5 plus 225 space equals space 337.5 space straight m squared$
Another way of finding the area of the pentagonal shape:

BY splitting the pentagonal shape into 3 triangles, we have:

Area of triangle I = $1 half cross times 15 cross times 15 space straight m squared space equals space 225 over 2 space straight m squared$

Area of trianlge II = $1 half cross times 15 cross times 15 space straight m squared space equals space 225 over 2 space straight m squared$

Area of triangle III = $1 half cross times 15 cross times 15 space straight m squared space equals space 225 over 2 space straight m squared$

∴ Area of the pentagonal shape = $space 225 over 2 space straight m squared space plus space 225 over 2 space straight m squared space plus space 225 over 2 space straight m squared space equals space 337.5 space straight m squared$
Jyoti’s diagram:The given shape is splitted into two congruent trap