Other tags that relate to Farhan's Poor Square
Sine, cosine, tangent. Area - triangles, quadrilaterals, compound shapes. Regular polygons and circles. Pythagoras' theorem. Similarity and congruence. Ratio and proportion. Triangles. Angle properties of polygons. Visualising. Mathematical reasoning & proof.There are 74 results
Broad Topics > Pythagoras and Trigonometry > Pythagoras' theorem
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?
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. . . .
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?
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?
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.
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 .
Garden Shed
Age 11 to 14
Challenge Level
Can you minimise the amount of wood needed to build the roof of my garden shed?
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.
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?
Circle Scaling
Age 14 to 16
Challenge Level
Describe how to construct three circles which have areas in the ratio 1:2:3.
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?
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.
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?
Squareo'scope Determines the Kind of Triangle
Age 11 to 14
A description of some experiments in which you can make discoveries about triangles.
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.
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?
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. . . .
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.
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.
The Dangerous Ratio
Age 11 to 14
This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.
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?
Two Circles
Age 14 to 16
Challenge Level
Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?
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? ...
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. . . .
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?
Pythagoras Proofs
Age 14 to 16
Challenge Level
Can you make sense of these three proofs of Pythagoras' Theorem?
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 ?
Crescents and Triangles
Age 14 to 16
Challenge Level
Can you find a relationship between the area of the crescents and the area of the triangle?
Medallions
Age 14 to 16
Challenge Level
Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?
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.
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?
Pythagorean Triples II
Age 11 to 16
This is the second article on right-angled triangles whose edge lengths are whole numbers.
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.
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.
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?
All Is Number
Age 7 to 14
Read all about Pythagoras' mathematical discoveries in this article written for students.
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!
Equilateral Areas
Age 14 to 16
Challenge Level
ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
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?
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?
Rectangular Pyramids
Age 14 to 18
Challenge Level
Is the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges?
Circle Box
Age 14 to 16
Challenge Level
It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
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?
Holly
Age 14 to 16
Challenge Level
The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.
Round and Round
Age 14 to 16
Challenge Level
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
Grid Lockout
Age 14 to 16
Challenge Level
What remainders do you get when square numbers are divided by 4?
Pareq Calc
Age 14 to 16
Challenge Level
Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
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?
Some(?) of the Parts
Age 14 to 16
Challenge Level
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Matter of Scale
Age 14 to 16
Challenge Level
Prove Pythagoras' Theorem using enlargements and scale factors.
NRICH is part of the family of activities in the Millennium Mathematics Project.