Answer:
6 ways
Step-by-step explanation:
Given:
Books: Spanish, Maths and History textbooks (1 each)
Required
Determine the number of arrangements
In total, Nathan has 3 books.
The number of arrangements (n) is as follows:
The first book can be lined in 3 ways
The second book can be lined in 2 ways
The third book can be lined in 1 way
So,
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