Question 1159866
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The y-coordinates of S and T are the same, so side ST is horizontal, with length 10-(-2) = 12.<br>
So we can use ST as the base; the height of the triangle is then just the distance from the line y=-2 to the point (4,4), which is 4-(-2) = 4+2=6.<br>
Then the area is one-half base times height: {{{(1/2)(12)(6) = 36}}}<br>
Alternatively (but I think it is more work), you could use the fact that it is a right triangle, with legs RS and RT, so the area is one-half the product of the lengths of those legs.<br>
The length of each leg is {{{6sqrt(2)}}}; then the area is {{{(1/2)(6sqrt(2))(6sqrt(2)) = (1/2)(72) = 36}}}<br>
But that, like I said, was more work....<br>