For the figures below, assume they are made of semicircles, quarter circles and squares. for each shape, find the area and perimeter. give your answer as a completely simplified exact value in terms of π (no approximations).

Part a) The area of the figure is

Part b) The perimeter of the figure is

Step-by-step explanation:

Step 1

Find the area of the figure

In this problem we have that

The figure ABC is the half of a square and the other figure is a semicircle

Find the area of the figure ABC

we have

The area of the half square ABC is equal to find the area of triangle ABC

so

Find the area of the semicircle

The area of the semicircle is equal to

we have that

substitute

The area of the figure is equal to

Step 2

Find the perimeter of the figure

The perimeter of the figure is equal to

we have

Applying Pythagoras theorem

Remember that

the circumference of a semicircle is equal to

The perimeter of the figure is equal to

Simplify

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: