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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Example 5: In the adjoining figure, RT and PU are the heights on sides S R
PQ and RQ, respectively of a parallelogram PQRS. The area of the
2
parallelogram is 1470 cm . If PQ = 49 cm and RQ = 35 cm, find the length U
of PU and RT.
Solution: In the given parallelogram, PQ = 49 cm, RQ = 35 cm. P T Q

We have, area of a parallelogram = Base × height
Area of parallelogram PQRS = PQ × RT
2
2
\ 1470 cm = 49 cm × RT (Area of the parallelogram = 1470 cm , given)
1470
So, RT = cm = 30 cm
49
Again, area of the parallelogram PQRS = RQ × PU

\ 1470 cm = 35 cm × PU
2
1470
So, PU = cm = 42 cm
35
Practice Time 10A

1. Mr Arora wants to build a home for his family. So, he bought a rectangular plot having a length of
60 ft and breadth of 40 ft. If the cost of the plot is `4500 per sq. ft, then find the total cost of the plot.
He wants to construct a house with dimension 30 ft × 20 ft in the middle of the plot and develop a
garden around the house. Find the total cost of developing a garden around the house at the rate of
`110 per sq. ft.

2. The area of a square park is the same as that of a rectangular park. If the side of the square park is
80 m, and the length of the rectangular park is 100 m, find the breadth of the rectangular park.

3. Two crossroads, each 12 m wide, cut at right angles through the centre of a
rectangular park of length 600 m and breadth 320 m and parallel to its sides 320 m
shown in the given figure. Find the area of the roads. Also, find the area of the
park excluding crossroads. 600 m
4. Find the area of each of the following parallelograms.
(a) (b) (c)

3 cm 4 cm 4 cm
2.8 cm
8 cm
5.5 cm
5. Find the area of the following triangles.
(a) (b) (c)

3.4 cm 3 cm 2.5 cm
5 cm 4 cm 4 cm
6. A floor tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is
2
10 cm. How many such tiles are required to cover a floor of an area of 1080 m ?
(Hint: Assuming the required no. of titles will fit exactly on the floor.)
7. From a circular card sheet of radius 28 cm, two circles of radius 7 cm and a rectangle of length
 22 
6 cm and breadth 2 cm are removed. Find the area of the remaining card sheet. Take π= 7  


233 Mensuration