Other tags that relate to Farhan's Poor Square
Mathematical reasoning & proof. Angle properties of polygons. Triangles. Pythagoras' theorem. Area - triangles, quadrilaterals, compound shapes. Similarity and congruence. Sine, cosine, tangent. Visualising. Regular polygons and circles. Ratio and proportion.There are 42 results
Broad Topics > Angles, Polygons, and Geometrical Proof > Triangles
Farhan's Poor Square
Age 14 to 16
Challenge Level
From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
Three Way Split
Age 14 to 16
Challenge Level
Take any point P inside an equilateral triangle. Draw PA, PB and PC from P perpendicular to the sides of the triangle where A, B and C are points on the sides. Prove that PA + PB + PC is a constant.
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.
A Shade Crossed
Age 14 to 16
Challenge Level
Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
Wedge on Wedge
Age 14 to 16
Challenge Level
Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?
Triangle in a Triangle
Age 14 to 16
Challenge Level
Can you work out the fraction of the original triangle that is covered by the inner triangle?
Arrh!
Age 14 to 16
Challenge Level
Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .
Hexy-metry
Age 14 to 16
Challenge Level
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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.
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.
Half a Triangle
Age 14 to 16
Challenge Level
Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
Equal Equilateral Triangles
Age 14 to 16
Challenge Level
Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?
Triangle Midpoints
Age 14 to 16
Challenge Level
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
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?
Kissing Triangles
Age 11 to 14
Challenge Level
Determine the total shaded area of the 'kissing triangles'.
Interacting with the Geometry of the Circle
Age 5 to 16
Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.
Making Maths: Equilateral Triangle Folding
Age 7 to 14
Challenge Level
Make an equilateral triangle by folding paper and use it to make patterns of your own.
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?
The Square Hole
Age 14 to 16
Challenge Level
If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?
Triangle Transformation
Age 7 to 14
Challenge Level
Start with a triangle. Can you cut it up to make a rectangle?
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. . . .
Lens Angle
Age 14 to 16
Challenge Level
Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
Triangular Tantaliser
Age 11 to 14
Challenge Level
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
Tricircle
Age 14 to 16
Challenge Level
The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .
Two Triangles in a Square
Age 14 to 16
Challenge Level
Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.
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?
Pareq Exists
Age 14 to 16
Challenge Level
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
Ratty
Age 11 to 14
Challenge Level
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?
LOGO Challenge 5 - Patch
Age 11 to 16
Challenge Level
Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
Dotty Triangles
Age 11 to 14
Challenge Level
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
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. . . .
Isosceles Triangles
Age 11 to 14
Challenge Level
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Xtra
Age 14 to 18
Challenge Level
Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.
Property Chart
Age 11 to 14
Challenge Level
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
Shapely Pairs
Age 11 to 14
Challenge Level
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
Constructing Triangles
Age 11 to 14
Challenge Level
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Counting Triangles
Age 11 to 14
Challenge Level
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Tetrahedra Tester
Age 11 to 14
Challenge Level
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
Calculating with Cosines
Age 14 to 18
Challenge Level
If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
NRICH is part of the family of activities in the Millennium Mathematics Project.