The measure of the consecutive sides of an isosceles trapezoid are in the ratio 8:5:2:5

the perimeter of the trapezoid is 140 inches if it's height is 20 inches find the area of the trapezoid

20x=140

x=7

so, the sides are 56,35,14,35

The bases are 56 and 14, so the area is (56+14)/2 * 20

The problem is, that if the sides are 35, the height is not 20. Fix that to get the true area.

1031.8

To find the area of the trapezoid, we need to use the formula:

Area = (1/2) * (b1 + b2) * h

Where:
b1 = base 1
b2 = base 2
h = height

Given information:
Height (h) = 20 inches
Perimeter = 140 inches
Ratio of the consecutive sides = 8:5:2:5

Step 1: Finding the bases of the trapezoid
Let's assume the sides of the trapezoid are 8x, 5x, 2x, and 5x.

The perimeter is the sum of all four sides:
Perimeter = 8x + 5x + 2x + 5x = 20x

Since the perimeter is given as 140 inches:
20x = 140

Divide both sides by 20:
x = 140 / 20
x = 7

Now we can find the bases:
Base 1 (b1) = 8x = 8 * 7 = 56 inches
Base 2 (b2) = 2x = 2 * 7 = 14 inches

Step 2: Calculating the area
We know that the height (h) is given as 20 inches.

Using the formula for the area of a trapezoid, substitute the values we found:
Area = (1/2) * (b1 + b2) * h
Area = (1/2) * (56 + 14) * 20
Area = (1/2) * 70 * 20
Area = 35 * 20
Area = 700 square inches

Therefore, the area of the trapezoid is 700 square inches.

To find the area of an isosceles trapezoid, you need to know the lengths of the parallel sides (bases) and the height.

In this case, we are given the ratios of the consecutive sides of the trapezoid, which are 8:5:2:5. Let's assign variables to these sides:

Let the consecutive sides be 8x, 5x, 2x, and 5x (since the ratio is 8:5:2:5).

We are also given that the perimeter of the trapezoid is 140 inches. The perimeter of a trapezoid is given by the sum of all its sides. In this case, the sum is:

8x + 5x + 2x + 5x = 140

Combining like terms, we have:

20x = 140

To solve for x, divide both sides of the equation by 20:

x = 140 / 20
x = 7

Now that we know the value of x, we can find the lengths of the consecutive sides:

8x = 8 * 7 = 56 inches
5x = 5 * 7 = 35 inches
2x = 2 * 7 = 14 inches
5x = 5 * 7 = 35 inches

The lengths of the sides are 56 inches, 35 inches, 14 inches, and 35 inches.

Next, we are given the height of the trapezoid, which is 20 inches.

To find the area of the trapezoid, we use the formula: Area = [(base1 + base2) * height] / 2

Plugging in the values, we get:

Area = [(56 + 35) * 20] / 2
Area = [91 * 20] / 2
Area = 1820 / 2
Area = 910 square inches

Therefore, the area of the trapezoid is 910 square inches.