Challenge Level

Can you calculate the length of this diagonal line?

Challenge Level

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

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

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

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

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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?

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

Challenge Level

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

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

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

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

Challenge Level

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

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

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

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

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

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

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

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

Challenge Level

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

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

Challenge Level

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?

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

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

Challenge Level

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

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

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

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

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

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

Challenge Level

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

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

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

Challenge Level

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?

Challenge Level

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?

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

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

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

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

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

Challenge Level

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

Challenge Level

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

Challenge Level

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