Find the perimeter of an isosceles trapezoid with base lengths of 10 and 18 and height of 8.
The top and bottom sides contribute 28 to the perimeter.
The two slanted sides have lengths that are the hypotenuses of a triangles with sides of 4 and 8. The hypotenuse is sqrt 80 = 8.944.
That makes the perimeter
28 + 2*8.944 = 45.89
To find the perimeter of the isosceles trapezoid, we need to add up the lengths of all four sides.
An isosceles trapezoid has two parallel sides, called the bases. In this case, we have two bases with lengths of 10 and 18.
Next, we need to find the lengths of the remaining two sides, which are the slanting sides. Since the trapezoid is isosceles, the slanting sides are equal in length.
The height of the trapezoid is given as 8 units. To find the length of the slanting side, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
In this case, the slanting side acts as the hypotenuse, and the height acts as one of the other sides. The length of the slanting side can be found using the formula:
Slanting side = √(height^2 + difference of base lengths^2)
Plugging in the values, we have:
Slanting side = √(8^2 + (18 - 10)^2)
= √(64 + 64)
= √128
= 8√2 (using the fact that √2 x √2 = 2)
Since we have two slanting sides, the total length contributed by the slanting sides is 2 * 8√2 = 16√2.
Now, we can find the perimeter by adding up all the sides:
Perimeter = Base 1 + Base 2 + Slanting side 1 + Slanting side 2
= 10 + 18 + 16√2 + 16√2
= 28 + 32√2
Therefore, the perimeter of the isosceles trapezoid with base lengths of 10 and 18 and height of 8 is 28 + 32√2 units.