Area and volume > Area 2-D shapes

Exercise 1

Exercise 2

All corners of this regular octagon lie on a circle with radius $5$ cm.

Compute the area of the white part that lies between the circle and the octagon.

Exercise 3

Somebody makes a three legged stool with a seat shaped as drawn here. This shape consists of a regular hexagon to three sides of which a segment of the circle through the corners of the hexagon has been added.

Compute both the circumference and the area of the seat.

Exercise 4

This symmetrical container is exactly half full with water. The length of the container is $2$ meters. The front and the rear are perpendicular to the bottom.

a

What is the depth of the water in the container?

b

What is the area of the water surface?