**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.