ABCD is an isosceles trapezoid with a height of 4 inches and bases of 10 and 12 inches .What is the perimeter of this trapezoid in inches and feet . HINT:Only the bottom of the entire figure is 16 inches long, not the top

First, we draw the trapezoid with the long base on the bottom. Using dotted lines, we draw 2 altitudes forming 2

congruent rt. triangles and a rectangle.

AE=ED = (AD-BC) / 2 = (12-10)/2 = 1in =
hor. sides of rt. triangles.

AB = CD = sqrt(1^2+4^2) = sqrt17 =
4.1in. = Length of non-parallel sides.

P = 4.1 + 10 + 4.1 + 12 = 30.2in.

To find the perimeter of the trapezoid, we need to add up the lengths of all of its sides. Since we are given the height and the lengths of the two bases, we can calculate the lengths of the slanted sides as well.

1. First, let's calculate the length of the slanted sides. Since the trapezoid is isosceles, the slanted sides are congruent.

We can use the Pythagorean theorem to find the lengths of these sides. Let's call the length of these sides "x."

Using the Pythagorean theorem, we have:
x^2 + 4^2 = (12 - 10)^2
x^2 + 16 = 4^2
x^2 + 16 = 16
x^2 = 0
x = 0 (since we cannot have a negative length)

This means that the slanted sides are actually horizontal segments, and their lengths are both zero inches.

2. Now, let's calculate the lengths of the bases. The bottom base is given as 16 inches, but only the length of the side that is parallel to the top base is considered.

Therefore, the length of the bottom base that contributes to the perimeter is 10 inches.

The top base measures 12 inches.

3. Finally, we can calculate the perimeter by adding up the lengths of all the sides:

Perimeter = length of bottom base + length of top base + 2 * slanted sides
Perimeter = 10 + 12 + 2 * 0 (since the slanted sides have length zero)
Perimeter = 22 inches

To convert inches into feet, we divide the length by 12 since there are 12 inches in a foot.

22 inches รท 12 = 1.83 feet (rounded to two decimal places)

Therefore, the perimeter of the trapezoid is 22 inches or 1.83 feet.