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.
Definition of 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 cm^{2}, 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 cm^{2}
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 m^{2}, 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 m^{2}
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.
After having gone through the stuff given above, we hope that the students would have understood "How to find the missing side length of a trapezoid"
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