The perimeter of a rectangular painting is 324 centimeters. if the width of the painting is 67 centimeters, what is its length?
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Looks like the larger triangle is equilateral (well, it must be, otherwise finding the area is impossible). That means the inradius is 6 and the outradius is 12, which is to say the altitudes (equal to the height, in this case) of this triangle have length 6 + 12 = 18.
In the smaller right triangle, the length of the missing leg is half the base of the larger triangle; call this length By the Pythagorean theorem,
Then the area of the larger triangle is