Find the area of a quadrilateral whose vertices have coordinates (8; 0), (10; 8), (2; 10), (0,2).

Let’s use the picture to solve the problem.

We need to find the area of ​​the filled square.

Let’s draw straight lines parallel to the coordinate axes from the top and right vertices of the square.

The result is a 10 x 10 cm square.

The desired area will be equal to the difference between the area of ​​a 10 x 10 square and four right-angled triangles, which are equal to each other in a right angle and two legs, the dimensions of which are 2 and 8 cm.

S = S1 – S2.

S1 = 10 * 10 = 100 cm2.

The area of ​​a right-angled triangle is half the product of the lengths of its legs. Then the area of ​​the four triangles is:

S2 = 4 * (1/2) * 2 * 8 = 32 cm2.

S = 100 – 32 = 68 cm2.

Answer: The area of ​​the quadrangle is 68 cm2.