Let's solve the problem step by step:

Part a: Find the area of the triangle

The formula for the area of a triangle is:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

• The given base $b = \frac{5}{4} \, \text{cm}$
• We need to find the height $h$.

Part b: Solve for the height $h$

Since the triangle forms a right triangle, we can use the Pythagorean theorem:

$h^2 + 1^2 = \left( \frac{3}{4} \right)^2$

Expanding each term:

$h^2 + 1 = \frac{9}{16}$

Subtracting 1 from both sides:

$h^2 = \frac{9}{16} - 1 = \frac{9}{16} - \frac{16}{16} = \frac{-7}{16}$

Since $h$ can't be imaginary, the area result depends on real. Let's step