distance for trapezoid?

Question

the parallel sides of the isosceles trapezoid shown are 10 ft long and 16 ft long, respectively. what is the distance between these two sides in feet?

(other sides are 5 ft)

Answer 1

Hi,

The height of an isosceles trapezoid is 4 feet.

If the 2 parallel sides are 16 and 10, then the longer side is 16 - 10 or 6 longer, 3 feet on each end.

To find the height, 3² + b² = 5²
9 + b² = 25
b² = 16
b = 4 This is the height.

I hope that helps!! :-)

Answer 2

4 feet.

The trapezoid can be divided into 2 right right triangles, one on each side, and a rectangle in the middle. since top and bottom are parallel and the other sides are equal, the two triangles are the same (well, one is flipped horizontally). The base of each triangle is then just (16 - 10)/2 or 3. You then have a triangle with two known sides: 3 and 5. The other side is the distance between the parallel sides of the trapezoid and can be found from:

c^2 = a^2 + b^2 with c = 5 and a (or b) = 3
25 = 9 + b^2
b^2 = 16
and b = 4

Answer 3

inside a isosceles trapezoid, there is a retangle, and two congruent triangles.

The whole bottom legth is sixteen. subtract the top legth (10) and you get 6. Divide the six in two for the base of the triangle.

So for the distance between the top and bottom is what you're looking for, so we'll call it X.

Use the Pathagrieum therum (a^2 + b^2 = c^2)

3^2 + X^2 = 5^2.

9+X^2=25

X^2 = 16

x=4.