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Find the area of this park using both ways. Can you suggest some other way of finding its area?

Answer :

(i) From Jyoti’s diagram:

We can observe that, Area of the pentagonal shape = Area of trapezium ABCD + Area of trapezium ADEF

\(= 2 \times Area \;of\; trapezium \;ABCD\)

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

\(= (15 + 30) \times 7.5\)

\(= 45 \times 7.5\)

\(= 337.5 m^2\)

So, the area of the pentagonal shape=337.5\(m^2\)

(ii) From Kavita’s diagram:

We can see that, area of the pentagonal shape = Area of triangle ABE + Area of square BCDE

\(=\frac { 1 }{ 2 }\times b \times h + 15 \times 15\)

\(=\frac { 1 }{ 2 }\times 15 \times 15 + 225\)

\(= 112.5 + 225= 337.5 m^2\)

So, the area of the pentagonal shape =\(337.5 m^2\)

Yes, there is other way to find the area which is as follows:

Required area ABCDEA=Area of rect. ABPQ-2\(\times\)area of triangle CPD

\(=(15\times 30)-(2\times \frac{1}2\times \frac{15}2)\)

\(=(450-\frac{225}2)=\frac{(900-225)}2m^2\)

\(=\frac{675}2m^2=337.5m^2\)

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- 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.
- 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.
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