Question 1
The diagonal of a quadrilateral is 30m in length and the length of the perpendiculars to it from the opposite vertices are 6.8 m and 9.6m. Find the area of the quadrilateral.Solution:
ABCD be the given quadrilateral BE âŠ¥ AC and DF âŠ¥ AC.
Let AC = 30m, BE = 6.8m, DF = 9.6m. Area of quadrilateral ABCD 
Question 2
Find the area of a rhombus the lengths of whose diagonals are 36cm and 22.5cm.Solution:
The area of the rhombus
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Question 4
Find the area of a trapezium whose parallel sides are 57 cm and 39 cm and the distance between them is 28 cm.Solution:
The area of the trapezium
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Question 6
The parallel sides of a trapezium are 25cm and 13cm. Its nonparallel sides are equal each being 10cm. Find the area of the trapezium.Solution:
AB = 25cm, DC = 13 cm, BC = 10 cm.
AD =10cm EB = AB  AE = AB  DC = 25  13 = 12cm CE = AD = 10cm. AE = DC = 13cm In Î” EBC, CE = BC = 10cm CF âŠ¥ AB, F is the midpoint of EB.
Area of trapezium = area of parallelogram AECD + area of Î” CEB

Question 7
Find the volume, the total surface area and the lateral surface of a cuboid which is 8m long, 6m broad and 3.5m high.Solution:
The volume of cuboid
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The total surface area of the cuboid
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The lateral surface area of the cuboid =
Question 10
An open rectangular cistern when measured outside is 1.35 m long 1.08m broad and 90cm deep and is made of iron which is 2.5cm thick. Find the capacity of the cistern and the volume of the iron used.Solution:
The external dimensions of the cistern are
Length = 135 cm, breadth = 108cm, depth = 90 cm.
External volume =
The internal dimensions of the cistern are
Length = (135  5) cm = 130 cm, breadth = (108  5) cm = 103cm
Height = (90  2.5) cm = 87.5 cm
The capacity of the cistern = internal volume of the cistern
Volume of iron = external volume  internal volume
Solution:
The area of the field
The area of the pit The area over which the earth is spread out
The volume of earth dug out âˆ´ The rise in level . 
Question 12
Find the volume of a cylinder which is 18cm in height and radius 10.5 cm.
Solution:
The volume of the cylinder
Question 13
How many cubic metres of earth must be dug out to since a well is 16m deep and which has a radius of 3.5m? If the earth taken out is spread over a rectangular plot of dimensions what is the height of the platform so formed?Solution:
The volume of the earth dug out
The area of the given plot
The volume of the platform formed = the volume of the earth dug out
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The height of the platform
The height of the platform = 1.54m.
Question 14
An iron pipe is 21cm long and its exterior diameter is 8cm. If the thickness of the pipe is 1cm and iron weighs 8g/cm^{3}. Find the weight of the pipe.Solution:
The external radius of the pipe = 4cm
The internal radius of the pipe = (4  1) cm = 3cm The external volume Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â The internal volume The volume of the metal = external volume  internal volume Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â The weight of the pipe = Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Question 15
A closed metallic cylindrical box is 1.25m high and it has a base whose radius is 35cm. If the sheet of metal costs Rs. 80 per m^{2}. Find the cost of the material used in the box. Find the capacity of box in litres.Solution:
The area of metal used = total surface area of the box
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The cost of material used =
The capacity of the box = volume of the box
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Question 16
A rectangular piece of paper of dimensions 22cm by 12cm. is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.Solution:
Length of paper = Height of the cylinder = 12cm
Circumference of its base = 22 cm
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Volume of the cylinder
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Question 17
PQRS is a quadrilateral in which PQ =4 cms, QR = 9.2 cms, RS = 8cm SP = 6cm âˆ PSR = âˆ PQR = 90Â° . Find its area.Solution:
Area of right angled
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Area of right angled
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Area of quadrilateral
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Question 18
Find the surface area of a chalk box whose length, breadth and height are 16cm, 8cm and 6cm respectively.Solution:
Chalk box is in the form of cuboid.
Surface area of the cuboid
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âˆ´ The area of the chalk box is 544 cm^{2}.
Question 20
The length of a hall is 20m and width 16m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height and volume of the hall?
Solution:
Let 'h' be the height of the wall.
Sum of areas of four walls
Sum of the areas of the floor and the flat roof =
Given that the sum of the areas of four walls is equal to the sum of the areas of the floor and roof
Volume of the hall .