MAR DIONYSIUS SENOIR SEC SCHOOL
RISHI VALLEY,
MALLAPALLY, Kerala, India-689534
Herons Formula
Paper : IX Mathematics Herons Formula
Q.1
Drawing room of Mr. Kapur has a triangular floor of dimensions 7 m, 8 m, 9 m respectively. He wants to cover it
with marble tiles of size 20 cm
25 cm. How many tiles does he need to purchase?
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Q.2
Chhotu''s shirt was torn while getting into a bus. He wants to cover the damaged part with a triangular sticker. If
the rate of sticker is Rs 40 per cm2 and the tailor stiches the sticker at the rate of Rs 10 per cm. Find the amount
chhotu has to spend to get repaired the damaged part of his shirt if the size of the sticker is
2 cm
3 cm
4 cm .
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Q.3
In the given figure
ADB =
BAC = 90o, AD = 3 cm, BD = 4 cm and
BC = 13 cm. Calculate the area of the shaded portion.
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Q.4
PQR is an equilateral triangle with each side 13 cm and a right angled
= 90o. Find the area of the shaded region.
QSR with side SR = 12 cm and
S
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Q.5
The perimeter of a triangular field is 450 m and its sides are in the ratio 13:12:5. Find the area of the
triangle.
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Q.6
If four isosceles right angled triangles of side 5 m are removed from the corners of a rectangular plot 20 m
m, then find the area of the remaining portion.
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Q.7
Find the area of a triangle, whose sides are in the ratio 9:40:41 and whose perimeter is 180 m.
Q.8
The length of the sides of a triangle are 5 cm, 12 cm and 13 cm. Find the length of the perpendicular, from the
opposite vertex, to the side whose length is 13 cm.
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Q.9
Find the area of a triangular field of sides 715 m, 660 m and 275 m. Also, find the cost of reaping the field at Rs
2.00 per 100 meters.
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Q.10
A triangle has sides of length 35 cm, 54 cm and 61 cm. Find its area. Also, find the smallest of its
altitudes.
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Q.11
The perimeter of a triangle is 44 cm and its sides are in the ratio 9:7:6. Find its area.
Q.12
10
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If each side of an equilateral triangle is increased by 2 cm, then its area is increases by
the length of each side and the area of the triangle.
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. Find
Q.13
The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs 24.60 per hectare
is Rs 332.10, find its base and height.
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Q.14
The height of a parallelogram is one-third its base. If the area is 108 cm2, find its base and height.
Q.15
If the diagonal of a square is twice the side of an equilateral triangle, find the ratio of the area of the triangle to
the area of the square.
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Q.16
The diagonal of a square A is (a + b). Find the diagonal of a square B whose area is twice the area of
A.
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Q.17
The diagonals of a rhombus are 15 cm and 36 cm long. Find its perimeter.
Q.18
A rectangular courtyard, 3.78 m long and 5.25 m broad, is to be paved exactly with square tiles, all of the same
size. Find the largest size of such a tile and the number of tiles required to pave it.
(Marks : 3 )
Q.19
A chess board contains 32 equal squares and the area of each square is 12.5 cm2. A border round the board is 2
cm wide. Find the length of side of chess board.
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Q.20
The area and perimeter of a rhombus are 2016 m2 , 260 m respectively find the length of
its diagonals.
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Q.21
Banwari has three sons. Before dying he wants to divide his courtyard among the sons. Such that the eldest son
Ghura gets the biggest part. Determine which part should be offered to Ghura if the dimensions of the courtyard
are as follows:
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Q.22
One side of a right triangle is 126 cm and difference of length of its hypotenuse and other side is 42 cm. Find the
measure of its unknown sides and calculate its area. Verify using Hero''s formula.
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Q.23
The perimeter of a triangular field is 240 dm. If two of its sides are 50 dm and 75 dm, find the length of the
perpendicular, on the side of length 50 dm, from the opposite vertex. Also, calculate the cost of watering the
field at Rs 2.75 per 100 dm2.
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Q.24
The perimeter of a right triangle is 60 cm. Its hypotenuse is 26 cm. Find the length of the other two sides and
the area of the triangle.
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Q.25
Find the percentage increase in the area of a triangle, if each side is doubled in length.
Q.26
There is a square field whose side is 44 m. A square flower bed is prepared in its centre leaving a gravel path all
round the flower bed. The total cost of laying the flower bed and gravelling the path at Rs 2.75 and Rs 1.50 per
square metre, respectively is Rs 4904. Find the width of the gravel path.
(Marks : 5 )
Q.27
Find the percentage decrease in area of a triangle if each of its sides is halved.
Q.28
The length of the sides forming the right angle of a right angled triangle are 5x cm and (3x - 1) cm. If the area
of the triangle is 60 cm2, find its hypotenuse.
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Q.29
A field is in the shape of a trapezium. Goal posts are made on the parallel sides. The players want to know the
distance between the goal posts. How can they do if they do not have measuring tapes etc, but they know the
dimension of the field as shown in the following figure:
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Q.30
ABCDEF is a painting in which different parts are painted in different colours. Find the total cost of painting if
ABDE is a square and the rate of painting is as follows:
red @ Rs 2 per cm2, green @Rs 2.5 per cm2, blue @Rs 1.5 per cm2, yellow @Re 1 per cm2.
(Marks : 5 )
Q.31
The dimension of a carpet spread in a puja pandal is shown below:
If a person can occupy an area of 0.5 m2, on an average, find the maximum number of persons who can sit in
the pandal at a time.
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Q.32
The cost of carpeting a room is Rs 72 and of papering the walls at 30 paise per square metreis Rs 102. The
length of the room is 18 m. If the width had been 4 m less, the cost of carpeting would have been Rs 18 less.
Find the height of the room.
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Q.33
The perimeter of one square is 748 cm and that of another is 336 cm. Find the perimeter and the diagonal of a
square whose area is equal to the sum of the areas of these two squares.
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Q.34
A rectangular lawn is 30 m by 20 m. It has two roads each 2 m wide running in the middle of it, one parallel to
the length and the other parallel to the breadth. Find the area of the roads.
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Q.35
The area of a rhombus is 2016 cm2 and its sides are equal to 65 cm. Find the length of its diagonals.
Q.36
The side of a square exceeds the side of another square by 4 cm and the sum of the areas of the two squares is
400 sq. cm. Find the dimensions of the 2 squares.
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Q.37
The sides of a field, in the form of a quadrilateral ABCD are AB = 25 m, BC = 60 m, CD = 39 m, and DA = 52 m.
The length of the diagonal AC = 65 m. Find the cost of ploughing it at 10 paise per square metre.
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Q.38
ABCD is a quadrilateral right angled at B, length of its sides AB, BC, CD and DA are 12 cm, 5 cm, 20 cm and 12
cm, respectively. Find the area of quadrilateral. If the area of this quadrilateral is equal to the area of a
parallelogram of base 12 cm find the height of parallelogram.
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Q.39
A Verandah 10.6 m long and 3.6 m broad is to be paved with equal square tiles. Find the least number of the
tiles required to pave the verandah. Also find the total cost, if the cost of paving 100 tiles is Rs. 6 only.
Q.40
The length of a rectangular field is increased by 50% and its breadth is decreased by 50% to form a new
rectangular field. Find the percentage change in the area of the field.
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Q.41
Find the area of trapezium whose parallel sides are 25 cm, 13 cm and other sides are 15 cm each.
Q.42
Find the area of the quadrilateral ABCD, in which AB = 7 cm, BC = 6 cm,
CD = 12 cm, DA = 15 cm and AC = 9 cm.
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