Don't wait for luck
Find area enclosed by in square units.
Details And Assumptions:
- is the distance of " " from origin. For example , and .
The answer is 12.
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1 solution
Moderator note:
Why does "space is bounded linearly" imply that we have a rhombus?
While I agree that we have a rhombus, there should be a better explanation of why.
Good observation of using the diagonals to find the area, instead of trying to hunt down the side lengths and angle inbetween.
Consider the boundaries of each dimension by making one component(the x and then the y) zero. This implies that ∣ x ∣ ≤ 2 and ∣ y ∣ ≤ 3 . Since this space is bounded linearly we should realize that we have a rhombus. The way to calculate the area for such a shape is by multiplying the length of the diagonals and then dividing that result by two. The diagonals are clearly of length 4 and 3 which can be surmised from the two inequalities derived earlier and making note that x can be both positive and negative.