Squares

problem

Logo Challenge - The Logic of Logo

Age

11 to 16

Challenge level

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
problem

Just Opposite

Age

14 to 16

Challenge level

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
problem
Favourite

Zig Zag

Age

14 to 16

Challenge level

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
problem

Folding Squares

Age

14 to 16

Challenge level

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
problem
Favourite

Semi-Detached

Age

14 to 16

Challenge level

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
problem

Folding Fractions

Age

14 to 16

Challenge level

What fractions can you divide the diagonal of a square into by simple folding?
problem

A Tilted Square

Age

14 to 16

Challenge level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
problem
Favourite

Vector Journeys

Age

14 to 18

Challenge level

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
problem

Trig Rules OK

Age

16 to 18

Challenge level

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
problem

A Swiss Sum

Age

16 to 18

Challenge level

Can you use the given image to say something about the sum of an infinite series?