Perimeter of a Trapezium

# Perimeter of a Trapezium

## 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.