Area - circles, sectors and segments

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

How could you find out the area of a circle? Take a look at these ways.

Investigate constructible images which contain rational areas.

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

If I print this page which shape will require the more yellow ink?

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Can you work out the shaded area surrounded by these arcs?

Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.