Other tags that relate to Tin Tight
Maths Supporting SET. Volume and capacity. Cubes & cuboids. Surface and surface area. Spheres, cylinders & cones. Similarity and congruence. Visualising. Ratio and proportion. Fractions. Pythagoras' theorem.There are 74 results
Broad Topics > Pythagoras and Trigonometry > Pythagoras' theorem
All Tied Up
Age 14 to 16
Challenge Level
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
Ball Packing
Age 14 to 16
Challenge Level
If a ball is rolled into the corner of a room how far is its centre from the corner?
Napkin
Age 14 to 16
Challenge Level
A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .
Rhombus in Rectangle
Age 14 to 16
Challenge Level
Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
Hex
Age 11 to 14
Challenge Level
Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
Squ-areas
Age 14 to 16
Challenge Level
Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . .
Inscribed in a Circle
Age 14 to 16
Challenge Level
The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?
Isosceles
Age 11 to 14
Challenge Level
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
The Spider and the Fly
Age 14 to 16
Challenge Level
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Square Pegs
Age 11 to 14
Challenge Level
Which is a better fit, a square peg in a round hole or a round peg in a square hole?
In a Spin
Age 14 to 16
Challenge Level
What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
Slippage
Age 14 to 16
Challenge Level
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .
At a Glance
Age 14 to 16
Challenge Level
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Where to Land
Age 14 to 16
Challenge Level
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
Nicely Similar
Age 14 to 16
Challenge Level
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
Six Discs
Age 14 to 16
Challenge Level
Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?
Pythagoras Proofs
Age 14 to 16
Challenge Level
Can you make sense of these three proofs of Pythagoras' Theorem?
Circle Packing
Age 14 to 16
Challenge Level
Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...
Star Gazing
Age 14 to 16
Challenge Level
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
Semi-square
Age 14 to 16
Challenge Level
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
Ladder and Cube
Age 14 to 16
Challenge Level
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
Garden Shed
Age 11 to 14
Challenge Level
Can you minimise the amount of wood needed to build the roof of my garden shed?
Under the Ribbon
Age 14 to 16
Challenge Level
A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?
Fitting In
Age 14 to 16
Challenge Level
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .
Are You Kidding
Age 14 to 16
Challenge Level
If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?
Cutting a Cube
Age 11 to 14
Challenge Level
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
Circle Scaling
Age 14 to 16
Challenge Level
Describe how to construct three circles which have areas in the ratio 1:2:3.
Liethagoras' Theorem
Age 7 to 14
Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.
Squareo'scope Determines the Kind of Triangle
Age 11 to 14
A description of some experiments in which you can make discoveries about triangles.
Partly Circles
Age 14 to 16
Challenge Level
What is the same and what is different about these circle questions? What connections can you make?
Pythagoras
Age 7 to 14
Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music.
Floored
Age 14 to 16
Challenge Level
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?
Kite in a Square
Age 14 to 16
Challenge Level
Can you make sense of the three methods to work out the area of the kite in the square?
Take a Square
Age 14 to 16
Challenge Level
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
A Chordingly
Age 11 to 14
Challenge Level
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
Medallions
Age 14 to 16
Challenge Level
Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?
The Pillar of Chios
Age 14 to 16
Challenge Level
Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
Weighty Problem
Age 11 to 14
Challenge Level
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Corridors
Age 14 to 16
Challenge Level
A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
The Old Goats
Age 11 to 14
Challenge Level
A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .
Circumnavigation
Age 14 to 16
Challenge Level
The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
Trice
Age 11 to 14
Challenge Level
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
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?
Matter of Scale
Age 14 to 16
Challenge Level
Prove Pythagoras' Theorem using enlargements and scale factors.
Where Is the Dot?
Age 14 to 16
Challenge Level
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
Tilting Triangles
Age 14 to 16
Challenge Level
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
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.
Pythagorean Triples I
Age 11 to 16
The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!
Pythagorean Triples II
Age 11 to 16
This is the second article on right-angled triangles whose edge lengths are whole numbers.
NRICH is part of the family of activities in the Millennium Mathematics Project.