This is going to be a quick post. This will cover consumer surplus when there is perfectly elastic demand.
When a market is characterized by inelastic demand, that means that consumers are perfectly sensitive to price. If the price increases above the equilibrium level, they will reduce the amount they purchase to zero.
For the given price, they will purchase an infinite amount. Therefore, it is not necessary to ever provide a price lower since you can already sell as much as you desire at the given price.
The above is a market characterized by inelastic demand. It is worth noting that the demand curve is perfectly horizontal. This shows us what was said above: that an increase in price above the market level will lead to consumption dropping to zero.
It should be recalled that the consumer surplus is defined as the difference between the willingness to pay and how much is actually paid. In the above example, the willingness to pay is always the same. And given that it coincides with the price, this means that the consumer surplus will be zero. Thus when demand curve is perfectly elastic, there will be no consumer surplus.
The area shaded in the green is the producer surplus. Because the price corresponds to the point where supply intersects demand on the price axis, we can find the shaded triangle below the demand curve when trying to solve for the producer surplus.
Another post which might be of interest is what is the producer surplus when supply is perfectly inelastic.