The area of a trapezium is 352 cm² and the distance between its parallel sides is 16 cm. If one of the parallel sides is of length 25 cm, find the length of the other.
Answers
Step-by-step explanation:
Given:-
The area of a trapezium is 352 cm² and the distance between its parallel sides is 16 cm. If one of the parallel sides is of length 25 cm.
To find:-
find the length of the other.
Solution:-
One of the parallel sides of a Trapezium is 25 cm
Let a=25 cm
Let the other Parallel side of the Trapezium= b cm
Distance between the two parallel sides=16 cm
h=16 cm
Area of a Trapezium=(1/2)h(a+b)=h(a+b)/2 sq.units
We have ,
a= 25 cm
b=b cm
h=16 cm
On Substituting these values in the formula
=>16(25+b)/2 sq.cm
=>8(25+b) sq.cm
=>200+8b sq.cm
Area of the Trapezium=8b+200 sq.cm
According to the given problem
Area of the Trapezium=352 cm²
=>8b+200=352
=>8b=352-200
=>8b=152
=>b=152/8
=>b=19
b=19 cm
Answer:-
The length of the other Parallel side of the Trapezium is 19 cm
Check:-
We have ,
a=25 cm
b=19 cm
h=16 cm
area of the Trapezium=h(a+b)/2 sq.units
=>16(25+19)/2 cm²
=>8(44) cm²
=>352 cm²
area of the Trapezium=352 cm²
Verified the relation .
Used formula :-
If "a" and "b" are the two parallel sides and "h" is the distance between them of the Trapezium then the area of the Trapezium is h(a+b)/2 sq.units
Step-by-step explanation:
let the length of other side be x cm
Area of Trapezium= 1/2 × sum of parallel sides × distance between parallel lines
352 cm² = 1/2 × (25+x)cm × 16cm
352 cm² = (25+x)cm × 8cm
352 cm²/8cm = 25cm + x cm
44cm = 25cm + x cm
44cm - 25cm = x cm
x= 19cm (length of other side)
Ans.- 19cm