Question

On a coordinate plane, parallelogram A B C D has points (3, 6), (6, 5), (5, 1), and (2, 2).

What is the area of parallelogram ABCD?

13 square units
14 square units
15 square units
16 square units

Answer 1

13 square units

Explanation:

The bounding rectangle is 4 units wide and 5 units high, so has an area of 4×5 = 20 square units. From that are subtracted the areas of 4 triangles. 2 of them are 3 wide and 1 high, so have a combined area of 3×1 = 3 square units. The other two are 1 wide and 4 high, so have a combined area of 1×4 = 4 square units.

Then the area of the parallelogram is ...

20 -3 -4 = 13 . . . . square units