Circles, Polygons and Area WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?

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Presentation transcript:

Circles, Polygons and Area WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?

The circle has a radius of 1 unit. 1

This is the only piece of information you will be given, other than explanations of mathematical vocabulary. 1

What is the area of the circumscribed square?

What is the area of the inscribed square?

What is the area of the circle?

Generalising USING SYMBOLS

The circle has a radius r. r

This is the only piece of information you will be given. r

What is the area of the circumscribed square?

What is the area of the inscribed square?

What is the area of the circle?

Extension questions HIGHER TIER

The circle has a radius of 1 unit. 1

What is the area of the inscribed equilateral triangle?

What is the area of the inscribed regular hexagon?

Some hints ADDING USEFUL LINES!

What is the perimeter of the inscribed equilateral triangle?

What is the perimeter of the inscribed equilateral triangle? The radius of the circle may help …

… especially if we draw 3 of them …

… and project the lines … … to create other triangles whose angles we can deduce … … and whose side lengths we can calculate.