2023 CSS AM S3 EOY Q4

A triangular prism with base length (2√5 + 3) cm, vertical height (3√5 - 2) cm, and length H cm.

The volume of the triangular prism shown below is \(\left( 159 + \frac{179}{2}\sqrt{5} \right)\) cm\({}^3\).

Find, without using a calculator, in the form of \(a + b\sqrt{5}\),

1. the cross-sectional area of the triangular prism,[2]
2. the height, \(H\) of the triangular prism.[3]