HOW TO FIND THE MISSING SIDE LENGTH OF A TRAPEZOID

Let us look at some examples to understand how to find the missing length side length of a trapezoid.

Example 1 :

The area of the trapezium field is 34 cm², the distance between two parallel sides is 4 cm one parallel side is 5 cm. Find the other parallel side.

Solution :

Let 'a' be the length of the parallel side given and 'b' be the length of the missing parallel side.  

Given : Area of a trapezium is 34 square cm.

Then, 

(1/2) (a + b) ⋅ h  =  34

Distance between parallel side (h)  =  4 cm and a  =  5. 

Then, 

(1/2) (5 + b) ⋅ 4  =  34

(5 + b) ⋅ 2  =  34

Divide each side by 2.

5 + b =  17

Subtract 5 from each side. 

b  =  17

b  =  12 cm

So, the length of other parallel side is 12 cm.

Example 2 :

The area of a trapezium shaped field is 480 m², the length of parallel sides are 20 m and 44 m. Find the distance between parallel sides.

Solution :

Given : Area of a trapezium is 480 m².

Then, 

(1/2) (a + b) ⋅ h  =  480

Substitute a = 20 and b = 44.

(1/2) (20 + 44)  ⋅ h  =  480

(1/2) (64) ⋅ h  =  480

 (32) ⋅ h  =  480

Divide each side by 32.

h  =  15

So, the distance between parallel sides is 15 m.

Example 3 :

In a trapezium the measurement of one parallel side two more than the other parallel side and the height is 4 cm. The area of the trapezium is 64 cm². Find the two parallel sides.

Solution :

Let  'a' and 'b' be the lengths of the two parallel sides of a trapezium. 

Given : One parallel side is two more than the other parallel side.

Then, 

b  =  a + 2

Given : Area of a trapezium is 64 square cm.

Then, 

(1/2) (a + b) ⋅ h  =  64

(1/2) (a + a + 2) ⋅ 4 = 64

(1/2) (2a + 2) ⋅ 4 = 64

2(2a + 2)  =  64

2a + 2  =  32

2a  =  30

 a  =  15 cm

Then, 

b  =  a + 2

b  =  15 + 2

b  =  17 cm

So, the two parallel sides are 15 cm and 17 cm.

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