An isosceles trapezoid has bases of length 20 and 12 centimeters and legs of length 11 centimeters what is the area of the trapezoid to the nearest tenth

From the Pythagorean theorem,

h=sqrt(c^2-1/4(b-a)^2),
(1)

so
A = 1/2(a+b)h
(2)
= 1/2(a+b)sqrt(c^2-1/4(b-a)^2).
copied and pasted from Googleing Isosceles Trapezoid and clicking on the 2nd one, Wolfram Math World. sqrt is how the square root symbols pasted in. So if you need more detail, go there, they rock!

To find the area of an isosceles trapezoid, you can use the formula:

Area = (base1 + base2) / 2 * height

In this case, the bases are 20 and 12 centimeters, and the legs are 11 centimeters. However, the heights of the trapezoid are not given.

To proceed, we need to determine the height of the trapezoid.

To do that, we can use the Pythagorean theorem. The legs, being congruent, will form right triangles with the height of the trapezoid. Applying the theorem:

a^2 + b^2 = c^2

where a and b are the legs and c is the height, we get:

11^2 + (20 - 12)^2 = c^2
121 + 8^2 = c^2
121 + 64 = c^2
185 = c^2

To extract the height, we find the square root of 185:

c = √185
c ≈ 13.6 (rounded to one decimal place)

Now that we have the height (c), we can substitute it into the formula to calculate the area:

Area = (base1 + base2) / 2 * height
Area = (20 + 12) / 2 * 13.6
Area = 32 / 2 * 13.6
Area = 16 * 13.6
Area ≈ 217.6 (rounded to one decimal place)

Therefore, the area of the isosceles trapezoid is approximately 217.6 square centimeters.