AREA OF PLANE FIGURES
A figure bounded by three or more straight lines is called
a plane figure. It is to be noted tha,t circle is also a plane
figure. In this section we shall be finding the perimeters
and areas of plane figures. Let us discuss relevant facts.
Perimeter : Perimeter of a plane figure is the measure
of the length of its boundary. The unit of perimeter is same
as the unit of length i.e. centimetere (cm), metre (m), kilomietre (km) etc.
Area : Area of a plane figure is the measure of the region enclosed by it. The various units of measuring area
are : 1 square cm (cm ), 1 square metre ( m ) , 1 hectare
etc.
2
2
(7) Trapezium : A trapezium is a quardrilateral two of
whose sides are parallel. A trapezium whose non - parallel
sides are equal is known as an isosceles trapezium.
(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 diameter of the circle.
(v) Length of the arc of a circle subtending an angle 6 at
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
(vi) Area of a sector of a circle subtending an angle 9 at
(vii) If two circles touch internally/externally then the
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
1. The perimeter of the floor of a room is 18 m. What is
the area of the walls of the room, if the height of the
room is 3 m ?
(l)21m
(2) 42 m
2
Let the radius of the circle A be r cm.
The radius (R) of circle B = 24 cm.
According to the question.
.*. Ratio of the circumferences
4. The length of the side of a square is 14 cm. Taking
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.
(3) 46 sq.cm.
(4) 48 sq.cm.
2
(3) 54 m
(4) 108 m
[SSC Graduate Level PT Exam, 04.02.2007
(First Siting)]
2
2
Four equal quadrants of circles are included inside the
square.
7. (2) Tricky Approach
Ratio of the circumferences
= Ratio of radii = 3 : 4
Negative sign shows a decrease.
9. If each side of a square is increased by 10% what is
the percentage of increase of the area ?
(1) 10
(2) 21
(3) 42
(4) 100
10. The area of an equilateraf tnangfe, inscnbed in a cir-
9. (2) Required percentage increase in area
6. A copper wire of length 36 m and diameter 2 mm is
melted to form a sphere. The radius of the sphere (in
cm) is
(1) 2.5
(2) 3
(3) 3.5
(4) 4
7. The ratio of the radii of two wheels is 3 : 4. The ratio
of their circumferences is
(1) 4 : 3
(2) 3 : 4
(3) 2 : 3
(4) 3 : 2
8. If the length of a rectangle is increased by 10% and
its breadth is decreased by 10%, the change in its
area will be
(1) 1% increase (2) 1% decrease
(3) 10% increase (4) No change
16 to 8 : 8SC Combined Graduate Level Tier-I Exam,
16.05.2010)
OBJECTIVE TYPE QUESTIONS
1. The lengths of the adjacent sides of a plot of land in
the form of a parallelogram are 1 5 m and 13 m. If a diagonal is 14 m, find it area.
(1) 8 4 sq. m
(2) 1 6 8 sq. m
(3) 2 5 2 sq. m
(4) 4 2 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) 2 0 m
(3) 2 5 m
(4) 5 0 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)3m
(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) 3 2 sq. m
(3) 3 9 . 2 sq. m
(4) 3 8 . 9 sq. m
6.1f the area of a regular hexagon is
(1) 16 m
(2) 17 m
(3) 15 m
(4) 18 m.
1 3 . If a square and a rhombus stand on the same
base, then the ratio of the area of the square and the rhomb u s is
(1) 1 : 1
(2) 1 : 2
(3) 1 : 4
(4) 1 : 3
1 4 . The side of an equilateral triangle is 6 cm. Find the
height of the triangle.
cm, find
I its side.
UJSm
(2) 6 m
(3) 4 m
(4) 2 m
7. The area of a circle inscribed in an equilateral triangle is 48n square units. T h e 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
the remaining area is
9. T h e perimeter of a square whose area is equal to
lthat of a circle with perimeter 2TDL is
1 0 . The cost of fencing a square garden is Rs. 4 0 0 at
the rate of Re. 1 per metre. T h e area of the garden in
square metres is
(1) 10
(2) 1 0
(3) 1 0
(4) 1 0
1 1 . T h e 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) 1 1 7 6 m
(2) 1 1 2 2 m "
(3) 1331 m
(4) 2 2 1 1 m
1 2 . A rectangular carpet h a s an area of 1 2 0 sq, m.
and a perimeter of 46 m. T h e length of its diagonal is
2
3
4
2
2
2
2
ANSWERS