Find the area of a trapezoid whose vertices have coordinates: (2: 3), (2; 5), (10; 1), (10; 7).

We have the coordinates of the vertices of the trapezoid:

(2; 3), (2; 5), (10; 1), (10; 7).

Initially, you can already see that the bases of the trapezoid are parallel to the Y axis, since the pairwise points have the same ordinates.

We find the lengths of the bases.

a = | y1 – y2 | = | 3 – 5 | = 2;

b = | y3 – y4 | = | 1 – 7 | = 6;

The height of the trapezoid is parallel to the X axis. Let’s find it:

h = | x1 – x3 | = | x2 – x4 | = | 2 – 10 | = 8.

Found all the required values. Find the area of the trapezoid.

S = 1/2 (a + b) * h = 1/2 * (2 + 6) * 8 = 32.

Enough coordinates to define the area without plotting.