Perimeter of a Trapezium
We know that a trapezium is a plane
figure or two-dimensional figure. One of the opposite sides of a trapezium are
parallel. Its diagonals are not equal in length.
In the figure given below AB is
parallel to CD.
The perimeter of a closed
two-dimensional figure is the length of its boundary. The units of measurement
of perimeter are the same as that of length, i.e. cm, m or km.
To find the perimeter of a
trapezium, we add the measures of all its sides.
Let we have to find the perimeter of a given trapezium ABCD.
Perimeter of trapezium ABCD = AB + BC + CD + DA
If the measures of four sides of a
trapezium are a, b, c and d, then
Perimeter of the trapezium = a + b
+ c + d
Thus, the perimeter of a
trapezium = a + b + c + d
Perimeter of a Trapezium Formula
Perimeter of a trapezium = a + b + c + d
Where a, b, c and d are the four sides
of the trapezium.
Perimeter of an Isosceles Trapezium Formula
If the non-parallel sides of a trapezium are equal, then the trapezium is called an isosceles trapezium.
Let in the above figure, AB = a, BC =
DA = b and CD = c.
Then perimeter of the trapezium = AB +
BC + CD + DA
= a + b + b + c
= a + 2b + c
Perimeter
of an isosceles trapezium = a + 2b + c
Where a and c are the length of the
parallel sides and b is the length of the equal non-parallel sides of the
trapezium.
Perimeter of a Trapezium Example
Example 1: Find
the perimeter of a trapezium whose four sides measure 5 cm, 6.5 cm, 7 cm and
5.5 cm.
Solution: Given:
a = 5 cm, b = 6.5 cm, c = 7 cm and d = 5.5 cm
Perimeter of a trapezium = a + b +
c + d
=
5 + 6.5 + 7 + 5.5
= 24
cm
Example 2: A
field is in the shape of an isosceles trapezium. The length of its parallel
sides are 60 m and 80 m. The lengths of its non-parallel sides are 50 m each.
Find the length of the rope required to fence all around it.
Solution: Given:
measure of the length of parallel sides = 60 m and 80 m
Measure of the length of non-parallel
sides = 50 m
Perimeter of the field = a + 2b + c
= 60 + 2 × 50 + 80 m
= 60 + 100 + 80 = 240 m
Hence, the total length of the rope
required to fence the field is 240 m.
Example 3: John jogs 8 rounds of a trapezium-shaped park whose sides
measure 50 m, 60 m, 75 m and 65 m. Find the total distance jogged by John in
kilometres.
Solution: Given: sides of the park = 50 m, 60 m, 75 m and 65 m
Distance covered by John
in 1 round = Perimeter of the park
= a + b + c + d
= 50 + 60 + 75 + 65
= 250 m
Total distance covered
by John in 8 rounds = 8 × 250 m = 2000 m
Thus, the total distance
covered in kilometres = 2000/1000 km
(Since 1 km = 1000 m)
= 2 km
Example 4: If the perimeter of an isosceles trapezium is 80 cm and its
parallel sides measure 15 cm and 25 cm, find the measures of each non-parallel
side.
Solution: Given: perimeter of the trapezium = 80 cm
Measure of the parallel sides = 15
cm and 25 cm
We know that,
Perimeter of an
isosceles trapezium = a + 2b + c
80 cm = 15 + 2b + 25
2b + 40 = 80
2b = 40 cm
b = 20 cm
Hence, the measure of
each non-parallel sides is 20 cm.
Example 5: A
photo frame is in the shape of a trapezium. Its four sides measure 25 cm, 30
cm, 28 cm and 32 cm. Find the cost of the frame at the rate of Rs 2 per cm.
Solution: Given:
measure of the sides = 25 cm, 30 cm, 28 cm and 32 cm
Perimeter of the photo frame = a + b +
c + d
=
25 + 30 + 28 + 32
= 115 cm
Cost of the frame = Rs 2 × 115 = Rs
230
Hence, the cost of the frame is Rs
230.