Example on Trapezoid Formulas

Example 1: Find the area of trapezoid if the bases are 10 cm and 16 cm. The shortest distance between the parallel sides is 8 cm.

Solution: 

Given lengths of bases,

• a = 10 cm
•  b = 16cm
• height h = 8cm

Area of Trapezoid = (1/2) h (a+b)

= (1/2) 8 (10+16)

= 140 cm²

Example 2: If the area of a trapezoid is given as 240 cm² and the sum of lengths of parallel sides is given as 30 cm, find the height of the trapezoid.

Solution:

Given,

• Area = 240 cm²
• (a+b) = 30 cm

Area of Trapezoid = (1/2) h (a+b)

240  = (1/2) h (30)

h = (240 × 2) / 30

h = 16 cm

Hence, the height of trapezoid is 16 cm

Example 3: Find perimeter of trapezoid if lengths of the sides are 15cm, 6cm, 12 cm, and 8 cm respectively.

Solution: 

Given,

• a = 15 cm
• b = 6 cm
• c = 12 cm
• d = 8 cm

Perimeter of Trapezoid = Sum of lengths of parallel sides and sum of lengths of non parallel sides

P = a + b + c + d

P = 15+6+12+8

P = 41 cm

Example 4: If the perimeter of a trapezium is 48 cm and the sum of parallel sides is 26 cm and the length of the Third side is 10 cm. Find the length of the fourth side.

Solution: 

Given,

• a+b = 26 cm
• c =10 cm
• Perimeter = 48 cm

Perimeter of Trapezoid = Sum of lengths of parallel sides and the sum of lengths of nonparallel sides

Perimeter of Trapezoid = a + b + c + d

48 = 26 + 10 + d 

d = 48- 26 – 10

= 12 cm

Hence the length of the fourth side is 12 cm

Example 5: If the length of a parallel side is greater than the other by 6 cm and the area of a trapezoid is 240 cm². Find the lengths of the parallel sides If the shortest distance between the parallel sides is 14 cm.

Solution:

Given,

• Area = 240 cm²
• Height = 14 cm

Let a parallel side a = x

According to given condition

b = x + 6

Area of trapezium = (1/2) h (a+b)

240 = (1/2) (14) (x + x + 6)

(240×2) / 14 = 2x + 6 

2x = 34.28 – 6

2x = 28.28

x = 14.14

Hence a = 14.14 cm

b = x + 6

b = 14.14 + 6

b = 20.14 cm

Hence 14.14 cm and 20.14 cm are the lengths of the parallel sides

Trapezoid is another name of trapezium and is a quadrilateral in which one pair of opposite sides are parallel. It is a quadrilateral and follows all the properties of a quadrilateral.

In this article we have covered, Trapezoid definition, types of trapezoid, properties of trapezoid, formulas of trapezoid and related example in detail.