The document contains information about geometric shapes such as circles, triangles, squares, rectangles, and parallelograms. It provides definitions and formulas for calculating properties of these shapes such as circumference, area, perimeter, and ratios of corresponding sides. It also includes examples of geometry problems and their step-by-step solutions.

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(10) Circle : A circle is the locus of a point which moves in a plane in such a way that its distance from a fixed point
always remains same. The fixed point is called the centre and the constant distance is known as the radius of the
circle. If r = radius, then,
(i) Circumference = 2itr or nd where d = 2r is the diam-
distance between their centres is equal to difference/sum
of their radii respectively.
(viii) Distance moved by a rotating wheel in one
revolution is equal to the circumference of the wheel.
(ix) The number Of revolutions completed by rotating
a wheel in one minute
(x) Angle described by minute hand in 1 hour = 360°
(xi) Angle described by hour hand in 12 hours = 360°
Remarks : (i) If the dimensions of a plane are given in
different units, care must be taken to express them in the
same unit before finding the area.
(ii) It should be noted carefully that 3 square metres and
3 metres square are different things. Three square metres
denote,an area 3 times as large as a square metre, whereas
three metres square denotes the area of a square whose
side is 3 metres. Obviously, 3 metres square is equivalent
to 9 square metres.
Solved Examples
eter of the circle .
v( ) Length of the arc of a circle subtendin g an angle 6 at
(vi) Area of a sector of a circle subtendin g an angle 9 at
(vii) If two circle s touc h internally/externall y the n th e

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1. The perimeter of the floor of a room is 18 m. What is
3. There are two concentric circles with outer circle
of radius 24 cm. If the area of the inner circle is onethird
of the area between the two circles, then find the ratio of
the circumference of the outer circle to that of the inner
circle.
(1) 1:2 (2) 2 : 1
(3) 3 : 4 (4) 4 : 3
Let the radius of the circle A be r cm. The radius (R) of
circle B = 24 cm.
vertices of the square as centres, 4 circles are drawn
each with a radius of 7 cm. Find the area of the region
of the square that remains outside the region of any the
circles.
(l)42sq.cm. (2) 44 sq.cm.
Accordin g to the question .
.*. Ratio of the circumference s
4. The lengt h o f the sid e o f a squar e i s 14 cm . Takin g
the area of the wall s of the room , i f the heigh t of the
room is 3 m ?
l)21m( 2
(2) 4 2 m 2
(3) 54 m 2
(4) 108 m 2
SS[ C Graduate Level PT Exam, 04.02.200 7
(First Siting)]
(3) 4 6 sq.cm . (4) 48 sq.cm .
Four equal quadrant s of circles are included inside the
square.

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OBJECTIVE TYPE QUESTIONS
1. The lengths of the adjacent sides of a plot of land in the
form of a parallelogram are 15m and 13 m. If a diagonal is 14 m,
find it area.
(1) 84 sq. m (2) 168 sq. m
(3) 252 sq. m (4) 42 sq. m
(2) The adjacent sides of a parallelogram are 25 cm
and 15 cm. The distance between the shorter sides is 20 cm,
determine the distance between the longer sides.
(1)6 cm (2) 8 cm
(3) 10 cm (4) 12 cm
3. A parallelogram and a rhombus are equal in area. The
diagonals of the rhombus are 88 m and 55 m respectively. One of
the sides of the parallelogram is 121 m, determine its
corresponding height.
(1) 10 m (2) 20 m (3) 25 m (4) 50 m
4. The cross section of a canal is a trapezium in shape. If the
canal is 10 m wide at top, 6 m wide at the bottom and the area of
cross-section is 72 sq. m ; determine its depth.
( l ) 3 m (2) 6 m
(3) 8 m (4) 9 m
5. A room measuring 7 m x 5.6 m is to be carpeted leaving
0.3 m space bare all around. Find, the carpeted area.
(1) 16 sq. m (2) 32 sq. m
(3) 39.2 sq. m (4) 38.9 sq. m
6.1f the area of a regular hexagon is cm, find
I its side.
U J S m (2) 6 m
(3) 4 m (4) 2 m
7. The area of a circle inscribed in an equilateral triangle is 48n
square units. The perimeter of the triangle is
(1) 72 linear units (2) 48 linear units (3) 36 linear units (4) 24
linear units 8. A rectangular sheet of card-board is 4 cm x 2 cm. Ihe
greatest possible circle is cut off from the card. Then

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the rate of Re. 1 per metre. The area of the garden in square metres
is
(1) 10 (2) 1 0 2 (3) 1 0 3 (4)
1 0 4
11. The length of a rectangular park is 50 m and its breadth is
20 m. There is a 7 m wide path all around it on the outside. Find
the area of the path.
(1) 1176 m 2 (2) 1122 m 2 "
(3) 1331 m 2 (4) 2211 m 2
12. A rectangular carpet has an area of 120 sq, m. and a
perimeter of 46 m. The length of its diagonal is
(1) 16 m (2) 17 m (3) 15 m (4) 18
m.
13. If a square and a rhombus stand on the same base, then
the ratio of the area of the square and the rhombus is
(1) 1 : 1 (2) 1 : 2
(3) 1 : 4 (4) 1 : 3
14. The side of an equilateral triangle is 6 cm. Find the
the remainin g are a is
9. Th e perimete r of a squar e whos e are a is equa l to
lthat of a circl e with perimete r 2TDL is
10 . Th e cos t of fencin g a squar e garde n is Rs . 40 0 at
heigh t o f th e triangle .
ANSWER S