Answer:
Perpendicular distance between the parallel sides = 9m
Step-by-step explanation:
- A trapezium is a quadrilateral, with one pair of its opposite sides being parallel, called its bases, and the other two non parallel sides called its legs.
- Area of trapezium is given by:
[tex]A=\frac{h}{2} (a+b)[/tex]
where a and b are the two parallel sides, and h is the perpendicular distance between the two parallel sides.
Step 1:
We have been given that:
Length of the top side, a = 17 m
Length of the bottom side, b = 15 m
Area of the trapezium, A = 144 m²
Step 2:
Substituting the above values into the area of the trapezium, to find the unknown value of the perpendicular distance, h:
[tex]A=\frac{h}{2} (a+b)[/tex]
[tex]144=\frac{h}{2} (17+15)[/tex]
[tex]144=\frac{h}{2} (32)[/tex]
[tex]16h=144[/tex]
[tex]h=\frac{144}{16}[/tex]
[tex]h=9m[/tex]
Therefore, the perpendicular distance between the parallel sides = 9 m
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