Other tags that relate to Pythagoras for a Tetrahedron
Sine rule & cosine rule. Mathematical reasoning & proof. Sine, cosine, tangent. Area - squares and rectangles. Triangles. 2D shapes and their properties. Polyhedra. Regular polygons and circles. Pythagoras' theorem. Circle properties and circle theorems.There are 8 results
Broad Topics > Measuring and calculating with units > Area - squares and rectangles
Pythagoras for a Tetrahedron
Age 16 to 18 Challenge Level:
In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation. . . .
Compare Areas
Age 14 to 16 Challenge Level:
Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
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.
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.
The Square Under the Hypotenuse
Age 14 to 16 Challenge Level:
Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?
Trig Rules OK
Age 16 to 18 Challenge Level:
Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
Warmsnug Double Glazing
Age 14 to 16 Challenge Level:
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
NRICH is part of the family of activities in the Millennium Mathematics Project.