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#### Resources tagged with Area - squares and rectangles similar to Areas and Ratios:

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### There are 8 results

Broad Topics > Measuring and calculating with units > Area - squares and rectangles

### Proof of Pick's Theorem

##### Age 16 to 18 Challenge Level:

Follow the hints and prove Pick's Theorem.

### Vecten

##### Age 16 to 18 Challenge Level:

Join in this ongoing research. Build squares on the sides of a triangle, join the outer vertices forming hexagons, build further rings of squares and quadrilaterals, investigate.

### 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...

##### Age 16 to 18 Challenge Level:

Find a quadratic formula which generalises Pick's Theorem.

### 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.

### 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?

### 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.

### 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. . . .