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Answer :

Given, area of trapezium field area=10500\(m^2\), Altitude of the field(h)=100m.

Let, the side of the trapezium near road be x cm and
the opposite parallel side = 2x m

We know, area of trapezium = \(\frac { 1 }{ 2 }\times (a + b) \times h\)

\(\Rightarrow 10500 = \frac { 1 }{ 2 }\times (2x + x) \times 100\)

\(\Rightarrow 2 \times10500 = 3x \times 100\)

\(\Rightarrow 21000 = 300x\)

\(\Rightarrow x = 70 m\)

So, the other side = \(2x = 2 \times 70 = 140 m\)

Hence, the required length of the side along the river= 140 m.

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