# Find the area of a trapezoid whose vertices have coordinates (0; 2) (10; 2) (10; 10) (2; 10)

October 5, 2021 | education

| The area of the trapezium C is equal to the half-sum of the bases a and b, multiplied by the height n.

C = (a + b) * n / 2. (1)

It remains to determine the parameters for formula (1) by the coordinates of the trapezoid points (0; 2), (10; 2), (10; 10), and (2; 10).

The first two points (0; 2), (10; 2) refer to the lower base, since they have one ordinate equal to 2, and = difference of abscissas = (10 – 0) = 10.

The upper two points are (10; 10), and (2; 10), they have a common ordinate of 10, in = (10 – 2) = 8.

Height n is equal to the difference between the ordinates of the upper and lower points:

n = (10 – 2) = 8.

Area C = (10 + 8) * 8/2 = 18 * 4 = 72.

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