Two cross sections along a roadway design project $-$ station $52+00$ and station $53+00-$ are depicted by the figures below. Calculate the following:

$($a$)$ Cross$-$sectional areas at the two stations.

$($b$)$ Volume of excavation between sta $52+00$ and sta $53+00$ using the average end area method.

$($c$)$ Volume of excavation between sta $52+00$ and sta $53+00$ using the prismoidal method.