Area - circles, sectors and segments
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problemTwo shapes and printer ink
If I print this page which shape will require the more yellow ink? -
problemMean geometrically
A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO? -
problemQuadarc
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS. -
problemGet cross
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing? -
problemRound and round
Prove that the shaded area of the semicircle is equal to the area of the inner circle. -
problemFloored
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? -
problemSquaring the circle
Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate. -
problemBound to be
Four quadrants are drawn centred at the vertices of a square . Find the area of the central region bounded by the four arcs.