2D shapes and their properties

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

In this problem, we're going to find sets of letter shapes that go together.

Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.

How many trapeziums, of various sizes, are hidden in this picture?

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?