1. There are 9 dots, and to make triangles, you need 3.

C(9, 3) is 84. However, out of these 84 ways, there are 3 horizontal lines, 3 vertical, and two diagonal (these aren't considered triangles).

Now, we can use complementary counting to find the remaining number of true cases.

84 - (3 + 3 + 2) = 84 - 8 = 76.

**Answer: 76 triangles**

2. If a right isosceles triangle were to have a hypotenuse of 1, we could find the values of the base and height using the Pythagorean Theorem.

\(x^2 + y^2 = 1^2 = 1\), \(x^2 + y^2 = 1\).

Now because the sides are the same length, we can simplify this equation to

\(2x^2 = 1\)

\(x^2 = \frac{1}{2}\), \(x = \sqrt{\frac{1}{2}}\).

To find the area, we use the area equation of a triangle (\(\frac{bh}{2}\)). Because the base and height are the same, the equation becomes \(\frac{b^2}{2}\) or \(\frac{h^2}{2}\).

Plugging the value we got into the equation, we get

\(\frac{\sqrt{\frac{1}{2}}^2}{2} = \frac{\frac{1}{2}}{2} = \frac{1}{4}.\)

**Answer: \(\mathbf{\frac{1}{4}}\)**

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