## About "How to find the missing side length of a trapezoid"

How to find the missing side length of a trapezoid:

Here we are going to see how to find the missing side length of a trapezoid.

Definition of trapezium :

The definition of trapezium is entirely different in both US and UK.

• In US a quadrilateral which is having no parallel sides is called trapezium.
• But in UK a quadrilateral which is having one pair of parallel sides is called trapezium.

Definition of trapezoid :

• In UK a quadrilateral which is  having no parallel sides is called trapezoid.
• But in US a quadrilateral which is having one pair of parallel sides is called trapezoid.

Now let us look into some example problems based on finding missing side of trapezium.

Question 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 :

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

Area of trapezium  =  34 cm2

Distance between parallel side (h)  =  4 cm

a  =  5 and b = ?

(1/2) (5 + b) ⋅ 4  =  34

(5 + b) ⋅ 2  =  34

Divide 2 on both sides

5 + b =  17

Subtract 5 on both sides

b  =  17 - 5  =  12 cm

Hence the length of other parallel side is 12 cm.

Question 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 :

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

Area of trapezium  =  480 m2

Distance between parallel side (h)  =  ?

a  =  20 m and b  =  44 m

(1/2) (20 + 44)  ⋅ h  =  480

(1/2) (64) ⋅ h  =  480

(32) ⋅ h  =  480

Divide 32 on both sides

h  =  480/32

=  15 m

Hence the distance between parallel sides is 15 m.

Question 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 :

Area of the trapezium = 64 cm²

Let  "a" and "b" are two parallel sides

One parallel side is two more than the other parallel side. So we can assume b as a + 2

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

(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

b = a + 2 ==> b = 15 + 2 ==> b = 17 cm

Hence the two parallel sides are 15 cm and 17 cm.

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