Question

the area of a Trapezium is 180 cm square and its height is 9 CM if one of the parallel sides is longer than the other by 6 cm find the two parallel sides

Answer 1

height of trapezium =9 cm
one of other side of trapezium is longer than 6 cm
one is 6cm and other is x+6
Area of trapezium =
1÷2 (sum of parallel sides )×height
1÷2 ( x + x+6) ×9 =180
1÷2 (2x+6)×9= 180
x+3×9=180
x+3=180÷9
x+3=20
x=20-3
x=17
one side is x = 17 cm
other side x+6 =17+6=23cm

Answer 2

Given: The area of a trapezium is 180 cm square and its height is 9 cm. One of the parallel sides is longer than the other by 6 cm.

To find: The length of the two parallel sides

Solution: Let the length of the smaller side be a.

Since the other parallel side is longer by 6 cm, the length of the longer side= x+6

Sum of parallel sides

= x+x+6

= 2x+6

Let height of the trapezium be denoted by h. Therefore, h = 9 cm

Area = 180 cm square

Area of trapezium is given by the formula:

$area = \frac{1}{2} \times (sum \: of \: parallel \: sides) \times height$

$= > 180 = \frac{1}{2} \times (2x + 6) \times 9$

$= > 2x + 6 = \frac{180 \times 2}{9}$

=> 2x+6 = 40

=> 2x = 40-6

=> 2x = 34

=> x= 34/2

=> x = 17

Therefore, length of shorter side= 17 cm

Therefore,

Length of longer side

=x+6

= 17+6

= 23 cm

Therefore, the length of the two parallel sides are 17 cm and 20 cm.