How do you know to add for the first one and multiply for the second??
1 answer:
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One way of solving this problem can be Heron's formula. It is a formula that allows us to compute the area of a triangle, knowing the length of its three sides.
For the sake of clarity, let's assume that the point in the top-left lies in the origin, and let's call it point A. Then, the "middle" point is point B, and the bottom-right point is point C.
If we fix the coordinate axis with the origin in A, we have the following coordinates for the three points:
We can compute the length of any side using the formula for the distance between two points:
Plugging the approriate values, we get the following lenghts:
Now that we have the lengths, we can use Heron's formula: given the side lenghts and the semiperimeter
, the area is given by
If you plug our values, you will get an area of 6.5. So, unless I'm mistaken, none of the answers seem to mach, whereas 7 seems the best approximation.