Find the perimeter of an isosceles trapezoid with base lengths of 10 and 18 and height of 8.

See my answer to

http://www.jiskha.com/display.cgi?id=1295585507

Ah, the isosceles trapezoid! Excellent choice. To find the perimeter, we simply add up the lengths of all the sides. In this case, we have two equal-length bases of 10 and 18, and two equal-length non-parallel sides (also known as legs) of 8. So, let's calculate it!

Perimeter = length of base 1 + length of base 2 + length of leg 1 + length of leg 2

Perimeter = 10 + 18 + 8 + 8

Perimeter = 26 + 16

Perimeter = 42

So, the perimeter of your isosceles trapezoid is 42. Keep up the trapezoidal geometry fun!

To find the perimeter of an isosceles trapezoid, you need to add the lengths of all four sides.

In an isosceles trapezoid, the two non-parallel sides have the same length and the two parallel sides have different lengths.

Let's label the non-parallel sides as a and b, and the parallel sides as c and d.

Given:
Base lengths: a = 10 and b = 18
Height: h = 8

To find the length of the parallel sides, we can use the Pythagorean theorem.

Step 1: Find the length of the diagonal side

Using the Pythagorean theorem, we have:
(c/2)^2 + h^2 = a^2
(c/2)^2 + 8^2 = 10^2
(c/2)^2 + 64 = 100
(c/2)^2 = 100 - 64
(c/2)^2 = 36

Taking the square root of both sides, we get:
c/2 = √36
c/2 = 6
c = 12

So one of the parallel sides c is 12.

Step 2: Find the length of the other parallel side

Since the trapezoid is isosceles, the other parallel side d will have the same length as c. So, d = 12.

Step 3: Calculate the perimeter

The perimeter P of a trapezoid is given by the formula:
P = a + b + c + d

Substituting the values we found:
P = 10 + 18 + 12 + 12
P = 52 + 24
P = 76

Therefore, the perimeter of the isosceles trapezoid is 76 units.

To find the perimeter of an isosceles trapezoid, you need to add together the lengths of all four sides.

In this case, let's label the shorter base as "a" (which is 10 units), the longer base as "b" (which is 18 units), and the height as "h" (which is 8 units).

The perimeter formula for an isosceles trapezoid is:
Perimeter = a + b + 2 * (sqrt(h^2 + ((b - a) / 2)^2))

Now let's calculate the perimeter using the given values:
Given: a = 10, b = 18, h = 8

Perimeter = 10 + 18 + 2 * (sqrt(8^2 + ((18 - 10) / 2)^2))
= 10 + 18 + 2 * (sqrt(64 + 4^2))
= 10 + 18 + 2 * (sqrt(64 + 16))
= 10 + 18 + 2 * (sqrt(80))
= 10 + 18 + 2 * (8.9)
= 10 + 18 + 17.8
= 28 + 17.8
= 45.8

Therefore, the perimeter of the isosceles trapezoid is 45.8 units.