What is the perpendicular distance (in cm) between the parallel sides of a trapezium whose area is 108sq cm and the lengths of the parallel sides are 9cm and 36cm?
- A3.6 cm
- B4.8 cm
- C7 m
- D4.8 m
Solution & Step-by-step Explanation
The formula for the area of a trapezium is given by:
Area=
2
1
×(Sum of parallel sides)×Perpendicular distance (h)
Given:
Area=108sq cm
Length of parallel sides (a and b) = 9cm and 36cm
Substitute the given values into the formula:
108=
2
1
×(9+36)×h
108=
2
1
×45×h
108×2=45×h
216=45h
h=
45
216
Dividing both numerator and denominator by 9:
h=
5
24
=4.8cm
Thus, the perpendicular distance between the parallel sides is 4.8cm.
Area=
2
1
×(Sum of parallel sides)×Perpendicular distance (h)
Given:
Area=108sq cm
Length of parallel sides (a and b) = 9cm and 36cm
Substitute the given values into the formula:
108=
2
1
×(9+36)×h
108=
2
1
×45×h
108×2=45×h
216=45h
h=
45
216
Dividing both numerator and denominator by 9:
h=
5
24
=4.8cm
Thus, the perpendicular distance between the parallel sides is 4.8cm.