MATHS
BOOKS - RS AGGARWAL MATHS (HINGLISH)
AREA OF A TRAPEZIUM AND A POLYGON
Solved Examples
1. Two parallel sides of a trapezium are of lengths 27 cm and 19 cm
respectively. and the distance between them is 14 cm. Find the area of the
trapezium.
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2. The area of a trapezium is 352cm and the distance between its parallel
2
sides is 16 cm. If one of the parallel sides is of length 25 cm, find the
length of the other.
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3. The area of a trapezium is 168cm
2
and its height is 8 cm. If one of the
parallel sides is longer than the other by 6 cm. Find the length of each of
the parallel sides.
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4. The parallel sides of a trapezium are 25cm and 13cm; its nonparallel
sides are equal, each being 10cm, find the area of the trapezium.
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5. ABCD is a trapezium in which AB || DC, ABデ78 cm, CD = 52 cm. AD = 28 cm
and BC =30cm . Find the area of the trapezium.
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6. The adjacent figure shows the diagram of a picture frame having outer
dimensions 28cm × 32cm and inner dimensions 20cm × 24cm . If the
width of each section is the same, find the area of each section of the
frame.
A. 112cm 2
96cm
2
B. 113cm 2
97cm
2
C. 114cm 2
98cm
2
D. 115cm 2
99cm
2
Answer: A
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7. In the given figure, ABCD is a quadrillateral in which
BD = 14cm, AL ⊥ BD, CM ⊥ BD such that AL = 6 cm and CM = 8 cm.
Find the area of aquad. ABCD.
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8. Find the area of the given pentagon ABCDE in which each one of BF, CH
and EG is perpendicular to AD such that AF = 9 cm, AG = 13 cm, AH = 19 cm,
AD = 24 cm, BF = 6 cm, CH = 8 cm and EG = 9 cm.
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9. Find the area of the given hexagon ABCDEF in which each one of BG, CI,
EJ and FH is perpendicular to AD and it is being given that AG = 6 cm, AH =
10 cm, Al = 18 cm, AJ = 21 cm. AD = 27 cm, BG = 5 cm, CI = 6 cm, EJ= 4 cm and
FH= 6 cm.
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10. In the given figure ABCDE is a pentagonal park in which DE = DC, AB =
BC = CE = EA = 25 m and its total height is 41 m. Find the area of the park.
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11. Find the area of the given hexagon ABCDEF in which each side
measures 5 cm, height BE = 11 cm and width FD = 8 cm.
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12. Find the area of an octagon ABCDEFGH having each side equal to 5 cm,
HC = 11 cm and AL ⊥ HC such that AL = 4 cm.
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Exercise 18 A
1. Find the area of a trapezium whose parallel sides are 24 cm and 20 cm
and the distance between them is 15 cm.
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2. Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3
cm and the distance between them is 16 cm.
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3. The shape of the surface of a table is trapezium. Its parallel sides are 1
m and 1.4 m and the perpendicular distance between them is 0.9 m. Find
its area.
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4. The area of a trapezium is 1080 cm
2
. If the length of its parallel sides
be 55 cm and 35 cm, then find the distance between the sides.
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5. A field is in the form of a trapezium. Its area is 1586m and the distance
2
between its parallel sides is 26 m. If one of the parallel sides is 84 m, find
the other.
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6. The area of a trapezium is 405cm . Its parallel sides are in the ratio 4 : 5
2
and the distance between them is 18 cm. Find the length of each of the
parallel sides.
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7. The area of a trapezium is 180cm
2
and its height is 9cm . If one of the
parallel sides is longer than the other by 6 cm, the length of the longer of
the parallel sides is
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8. In a trapezium-shaped field, one of the parallel sides is twice the other.
If the area of the field is 9450m
2
and the perpendicular distance between
the two parallel sides is 84 m, find the length of the longer of the parallel
sides.
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9. The length of the fence of a trapezium - shaped field ABCD is 130 m and
side AB is perpendicular to each of the parallel sides AD and BC. If BC = 54
m, CD = 19 m and AD = 42 m, find the area of the field.
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10. In the given figure, ABCD is a trapezium in which
AD ∣ ∣ BC, ∠ABC = 90
∘
, AD = 16cm, AC = 41cm and BC = 40 cm.
Find the area of the trapezium.
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11. 11. The parallel sides of a trapezium are 20 cml and 10 cm. Its
nonparallel sides are both equal. each being 13 cm. Find the area of the
trapezium.
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12. Find the area of a trapezium parallel sides are 11 cm and 25 cm long
and nonparallel sides are 15 cm and 13 cm .
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Exercise 18 B
1. In the given figure, ABCD is a quadrillateral in which AC = 24 cm,
BL ⊥ AC and DM ⊥ AC such that BL = 8 cm and DM = 7 cm. Find the
area of quard. ABCD.
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2. In the given figure, ABCD is a quadrilateral - shaped field in which
diagonal BD is 36 m, AL ⊥ BD and CM ⊥ BD such that AL = 19 m and
CM = 11 m. Find the area of the field.
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3. Find the area of pentagon ABCDE in which BL ⊥ AC, DM ⊥ AC and
EN ⊥ AC such that AC = 18 cm, AM = 14 cm, AN = 6 cm, BL = 4 cm, DM = 12
cm and EN = 9 cm.
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4. Find the area of hexagon ABCDEF in which
BL ⊥ AD, CM ⊥ AD, EN ⊥ AD and F P ⊥ AD such that
AP = 6cm, P L = 2cm, LN = 8cm, N M = 2cm, M D = 3cm, F P = 8cm
and CM = 6cm.
A. 200cm 2
B. 245cm 2
C. 234cm 2
D. 265cm 2
Answer: D
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5. Find the area of pentagone ABCDE in which BL ⊥ AC, CM ⊥ AD
and EN ⊥ AD such that AC = 10 cm, AD = 12 cm, BL = 3 cm, CM = 7 cm
and EN = 5 cm.
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6. Find the area enclosed by the given figure ABCDEF as per dimensions
given herewith.
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7. Find the area of given figure ABCDEFGH as per dimensions given in it.
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8. Find the area of a regular hexagon ABCDEF in which each side
measures 13 cm and whose height is 23 cm, as shown in the given figure.
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Exercise 18 C Objective Questions
1. The parallel sides of a trapezium measure 14 cm and 18 cm and the
distance between them is 9 cm. The area of the trapezium is
A. 96cm 2
B. 144cm 2
C. 189cm 2
D. 207cm 2
Answer: B
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2. The lengths of the parallel sides of a trapezium are 19 cm and 13 cm
and its area is 128cm . The distance between the parallel sides is
2
A. 9 cm
B. 7 cm
C. 8 cm
D. 12.5 cm
Answer: C
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3. The parallel sides of a trapezium are in the ratio 3:4 and the
perpendicular distance between them is 12 cm. If the area of the
trapeziumis 630cm , then its shorter parallel side is
2
A. 45 cm
B. 42 cm
C. 60 cm
D. 36 cm
Answer: A
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4. The area of a trapezium is 180cm
2
and its height is 9cm . If one of the
parallel sides is longer than the other by 6 cm, the length of the longer of
the parallel sides is
A. 17 cm
B. 23 cm
C. 18 cm
D. 24 cm
Answer: B
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5. In the given figure, AB ∣ ∣ DC and DA ⊥ AB . IF
DC = 7cm, BC = 10cm, AB = 13cm and CL ⊥ AB , the area of
trapezium ABCD is
A. 84cm 2
B. 72cm 2
C. 80cm 2
D. 91cm 2
Answer: C
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Test Paper 18 A
1. The base of a triangular field is three times its height and its area is
1350m
2
. Find the base of the field.
A. 30 m
B. 90 m
C. 40 m
D. 50 m
Answer: B
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2. Find the area of an equilateral triangle of side 6 cm.
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3. the perimeter of a rhombus is 180 cm and one of its diagonals is 72 cm
find the length of the other diagonal
A. 54 cm
B. 60 cm
C. 70 cm
D. 84 cm
Answer: A
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4. The area of a trapezium is 216m
2
and its height is 12m. If one of the
parallel sides is 14 m less than the other, find the length of each of the
parallel sides.
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5. Find the area of a quadrilateral one of whose diagonals is 40 cm and
the lengths of the perpendiculars drawn from the opposite vertices on
the diagonal are 16 cm and 12 cm.
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6. A field is in the form of a right triangle with hypotenuse 50 m and one
side 30 m. Find the area of the field.
A. 800 m 2
B. 619 m 2
C. 670 m 2
D. 600 m 2
Answer: D
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Test Paper 18 B Mark Against The Correct Answer In Each Of The Following
1. The base of a triangle is 14 cm and its height is 8 cm. The area of the
triangle is
A. 112cm 2
B. 56cm 2
C. 122cm 2
D. 66cm 2
Answer: B
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2. The base of a triangle is four times its height and its area is 50m
2
. The
length of its base is
A. 10 m
B. 15 m
C. 20 m
D. 25 m
Answer: C
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3. The diagonal of a quadrilateral is 20 cm in length and the lengths of
perpendiculars on it from the opposite vertices are 8.5 cm and 11.5 cm.
The area of the quadrilateral is
A. 400cm 2
B. 200cm 2
C. 300cm 2
D. 240cm 2
Answer: B
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4. Each side of a rhombus is 15 cm and the length of one its diagonals is
24 cm. The area of the rhombus is
A. 432cm 2
B. 216cm 2
C. 180cm 2
D. 144cm 2
Answer: B
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5. The area of a rhombus is 120cm
2
and one of its diagonals is 24 cm.
Each side of the rhombus is
A. 10 cm
B. 13 cm
C. 12 cm
D. 15 cm
Answer: B
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6. The parallel sides of a trapezium are 54 cm and 26 cm and the distance
between them is 15 cm. The area of the trapezium is
A. 702cm 2
B. 810cm 2
C. 405cm 2
D. 600cm 2
Answer: D
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7. The area of a trapezium is 384 cm . Its parallel sides are in the ratio 3:5
2
and the perpendicular distance between them is 12cm. Find the length of
the longer parallel sides.
A. 24 cm
B. 40 cm
C. 32 cm
D. 36 cm
Answer: B
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Test Paper 18 C Fill In The Blanks
1
1. (i) Area of triangle = × (…. . ) × (…. . ) .
2
1
(ii) Area of a ∣ ∣ gm = × (……) × (……) .
2
1
(iii) Area of a trapezium = × (……) × (……) .
2
(iv) The parallel sides of a trapezium are 14 cm and 18 cm and the distance
between them is 8 cm. The area of the trapezium is ……. cm . 2
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