Area of Trapezium, CBSE
Area of a Trapezium,
CBSE NCERT (Class 8, 9,10)
Here, DM and
CL are height or altitude of the trapezium ABCD.
Isosceles Trapezium: A trapezium is said to be an
isosceles trapezium if its nonparallel sides are equal.
Area of a Trapezium= ½(sum of parallel sides) (distance between
them)
= {½(AB+DC)h}
sq units
1. Find the area of a trapezium
whose parallel sides are 24 cm and 20 cm and the distance between them is 15
cm.
Answer:
Area of the
trapezium = ½ (sum of the parallel sides)(distance between them)
= {½(24+20)x15} cm²
=(½
x 44 x
15 ) cm²
= 22
x 15 cm²
= 330 cm²
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.
Answer:
Area of the
trapezium = ½ (sum of the parallel sides)(distance between them)
= {½(38.7+22.3)x16} cm²
=(½
x 61 x 16 ) cm²
= 61
x 8 cm²
= 488 cm²
3. The shape of the top surface of
a table is trapezium. Its parallel sides are 1m and 1.4m and the perpendicular
distance between them is 0.9m. Find its area.
Answer:
Area of the
trapezium = ½ (sum of the parallel sides)(distance between them)
= {½(1+1.4)x0.9} m²
=(½
x 2.4 x 0.9 ) m²
= 1.2 x 0.9 m²
= 1.08 m²
4. The area of a trapezium is 1080
cm². If the lengths of
its parallel sides be 55cm and 35cm, find the distance between them.
Answer:
Let the
distance between the two parallel sides be y cm.
Then, the
area of the trapezium = {½
x (55+35) x y }
= 45y cm²
But, the
area of the trapezium = 1080 cm². (given)
Therefore,
45y = 1080
→ y = 1080/45
→ y = 24 cm
5. A field is in the form of a
trapezium. Its area is 1586 m² and the distance
between its parallel sides is 26 m. If one of the parallel sides is 84 m, find
the other.
Answer:
Let the
length of the required side be y m.
Then, the
area of the trapezium = {½
x (84+y) x 26 }
= 13 x (84+y)
= (1092 + 13y) m²
But the area
of the trapezium = 1586 m² (given)
Therefore,
1092+13y = 1586
→ 13y = 494
→ y = 38 m
6. The area of a trapezium is 405 cm².
Its parallel sides are in the ratio 4:5 and the distance between is 18 cm. Find
the length of each of the parallel sides.
Answer:
The ratio of the parallel sides are 4:5
If one side is 4y cm then the other
one is 5y cm
The area of the trapezium = {½ x
(4y+5y) x 18 }
= 9 x 9y
= 81y cm²
But the area of the trapezium = 405 cm²
Therefore, 81y = 405
→ y = 5
Therefore, two parallel sides are 20
cm and 25 cm
7. The area of a trapezium is 180 cm² and
its height is 9 cm. If one of the parallel sides is longer than the other by 6
cm, find the two parallel sides.
Answer:
Let the shorter parallel sides is y cm
Longer side is (y+6) cm
The area of the trapezium = {½ x
(y+y+6) x 9 }
= 9/2 x (2y+6)
= (9y+27) cm²
But the area of the trapezium = 180 cm²
Therefore, 9y+27 = 180
→ 9y = 153
→ y = 17
Therefore, two parallel sides are 17
cm and 23 cm
8. In a trapezium-shaped field, one of the
parallel sides is twice of the other. If the area of the field is 9450 m² and
the perpendicular distance between the two parallel sides is 84 m, find the
length of the longer of the parallel sides.
Answer:
Let the two parallel sides are ‘y’ and
‘2y’
Therefore, the area of the trapezium
= {½ x
(y+2y) x 84 }
= 42 x
3y
= 126y m²
But the area of the trapezium = 9450 m²
Therefore, 126y = 9450
→ y = 75
Therefore, the longer side is (75 x 2) = 150 cm
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.
10. In the given figure, ABCD is a
trapezium in which ADIIBC, ∟ABC=90⁰, AD= 16 cm, AC = 41 cm and BC = 40 cm. Find
the area of the trapezium.
11. The parallel sides of a trapezium are
20 cm and 10 cm. Its parallel sides area both equal, each being 13 cm. Find the
area of the trapezium.
12. The parallel sides of a trapezium are
25 cm and 11 cm, while its nonparallel sides are 15 cm and 13 cm. Find the area
of the trapezium.
MCQ Questions with Answers
MCQ Questions with Answers
