Answer:
40 square units
Step-by-step explanation:
The area of a rectangle drawn on a coordinate grid can be found several ways. There are formulas for finding area from vertex coordinates. Pick's theorem can find the area from the number of boundary points and internal points where grid lines cross. The area formula that uses rectangle side lengths can also be used. And the figure can be decomposed into pieces whose area is easy to compute.
Strategy
When we plot the given points on a coordinate grid, we notice that one of the diagonals (TO) is a horizontal line. This suggests that the last of the strategies listed above may be the easiest to use. The length of that horizontal line is easy to find, and it divides the area into two congruent triangles.
Execution
The difference in x-coordinates of the points T and O give the length of segment TO: 4 -(-6) = 10.
The difference in y-coordinates of points Y and O give the height of the triangle that is half the rectangle: height = 10 -6 = 4.
The areas of each of the two triangles ΔTYO and ΔOCT will each be given by the formula ...
A = 1/2bh
Since there are two identical triangles, the total area is ...
A = 2(1/2)bh = bh
Using the base and height we found above, the area is computed to be ...
A = (10)(4) = 40 . . . . square units
The area of rectangle TYOC is 40 square units.
