HOW TO FIND THE MISSING SIDE LENGTH OF A TRAPEZOID
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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