Question

What is the area of the rectangle shown on the coordinate plane? Do not round at any steps.

Answer 1

`42`

Explanation:

We can inscribe this rectangle in a `10xx10` square with vertices `(2, -8)`, `(12, -8)`, `(12, 2)`, `(2, 2)`.

Then we see that the area of the rectangle is the area of the square less four isosceles right angled triangles, which can be combined into a `3xx3` square and a `7xx7` square.

Hence the area of the rectangle is:

`10^2-3^2-7^2 = 100-9-49 = 42`