a trapezium of area 105cm has parellel sides of length 5cm and 9cm. how far apart are the parallel sides?

Question

huh?

h=1/2x????????? i'm confused from ther on:s

Answer 1

Assume you mean 105 cm sq for area. If so, the parallel sides are 17 cm apart. Visualize it this way: You have one side 5 cm (given). The opposite side is 9 cm (given), or 4 cm longer. The longer side "sticks out" 2 cm on each side of the 5 cm side. Now draw a mental line from the ends of the 5 cm side perpendicular to the base (the 9 cm) That gives you a rectangle that is 5 cm by your unknown in area. the two 2 cm sections on each side form triangles with your mewntal line and the other two sides of the trapezium. The area of one of those triangles is 1/2 the base (that's 1, which is 1/2 of 2) times the height, which is again your unknown. Add all those together, and that's your total area:

5 times X plus 1/2(2) times X plus 1/2(2) times X = 105

5X + X + X = 105

7X = 105

X = 15cm

Answer 2

The area of a trapezoid (which I assume a trapezium is the same as) is equal to (x+y)/2 * H, where x is the length of the top, y is the length of the bottom, and H is the height.

Therefore,

A = (x+y)/2 * H

We know the area A = 105, and we know x and y (5 and 9 respectively). So we just plug it in.

105 = (5 + 9)/2 * H
105 = 14/2 * h
105 = 7h
105/7 = h

Therefore, h = 105/7, which represents the height, which represents how far apart the parallel sides are.

Answer 3

You need to use the formula for area of a trapezium.
Ar(trapezium) = 1/2 * (Sum of bases) * (Height)
You need the height
105 = 1/2(5 + 9)(h)
105 = 1/2(14)(h)
105 = 7h
h = 105/7
h = 15
The two bases are 15 cm apart.

Answer 4

This isn't all that complicated. You just make the 'zoid into a square by averaging the lengths of the parallel sides. (5+9 divided by 2) Then divide the area by the answer (7) and you get the length of the unknown side. (15) Ya?

OK. I wrote square when I should have wrote rectangle. Sue me.

Answer 5

Area = (1/2)(h(a + c))

105 = (1/2)h(5 + 9)
210 = 14h
h = 15

The lines are about 15 cm apart.

Answer 6

I am assuming the British defintion of trapezium, which is equivalent to an American trapezoid.
* * I tried to draw a diagram here, but I couldn't figure out how to insert spaces. So: Call the lengths of the two parallel sides b1 and b2, the distance between them h, and the area A. **
A=(1/2)(b1+b2)h
A=105
b1=5
b2=9
105=(1/2)(5+9)h=(1/2)(14)h=7h
105=7h
Divide both sides of the equation by 7.
15=h
_________
Or solve for h before substituting values
A=(1/2)(b1+b2)h
2A=(b1+b2)h
Divide by (b1+b2) on both sides of the equation.
2A/(b1+b2)=h
h=2A/(b1+b2)
h=2(105)/(5+9)
h=2(105)/14
h=210/14
h=15