If the midpoints of the sides of a right angled triangle are joined, what is the perimeter of this new triangle?

If two of the sides of a right-angled triangle are 5cm and 6cm long, how many possibilities are there for the length of the third side?

A 3x8 rectangle is cut into two pieces... then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?

Can you calculate the length of this diagonal line?

Can you work out the area of this isosceles right angled triangle?

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

A parallelogram is formed by joining together four equilateral triangles. What is the length of the longest diagonal?

A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?

How does the perimeter change when we fold this isosceles triangle in half?

Two arcs are drawn in a right-angled triangle as shown. What is the length $r$?

What is the perimeter of this unusually shaped polygon...

This quadrilateral has an unusual shape. Are you able to find its area?

A vine is growing up a pole. Can you find its length?

A palm tree has snapped in a storm. What is the height of the piece that is still standing?

This diagram has symmetry of order four. Can you use different geometric properties to find a particular length?

Can you work out the radius of a circle from some information about a chord?

Can you find the length of the third side of this triangle?

Triangle T has sides of lengths 6, 5 and 5. Triangle U has sides of lengths 8, 5 and 5. What is the ratio of their areas?

A square has area 72 cm$^2$. Find the length of its diagonal.

Work your way through these right-angled triangles to find $x$.

A rectangular piece of paper is folded. Can you work out one of the lengths in the diagram?

A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?

What does Pythagoras' Theorem tell you about the radius of these circles?

Can you find all the integer coordinates on a sphere of radius 3?

The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?

A window frame in Salt's Mill consists of two equal semicircles and a circle inside a large semicircle. What is the radius of the circle?

Can you find the length and width of the screen of this smartphone in inches?

The diagram shows a semi-circle and an isosceles triangle which have equal areas. What is the value of tan x?

Can you find the distance from the well to the fourth corner, given the distance from the well to the first three corners?

Two ribbons are laid over each other so that they cross. Can you find the area of the overlap?

The top square has been rotated so that the squares meet at a 60$^\text{o}$ angle. What is the area of the overlap?

Two circles touch, what is the length of the line that is a tangent to both circles?

Can you find the perimeter of the pentagon formed when this rectangle of paper is folded?

The diagram shows 8 shaded squares inside a circle. What is the shaded area?

How much of the inside of this triangular prism can Clare paint using a cylindrical roller?

The diagram shows two semicircular arcs... What is the diameter of the shaded region?

When you pull a boat in using a rope, does the boat move more quickly, more slowly, or at the same speed as you?

The diagrams show squares placed inside semicircles. What is the ratio of the shaded areas?

Can you find the radius of the larger circle in the diagram?

Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

Can you work out the length of the diagonal of the cuboid?

Calculate the ratio of areas of these squares which are inscribed inside a semi-circle and a circle.

How do these measurements enable you to find the height of this tower?