my son has to work out the area of a octagon with a outside perimeter of 1,000 metres,

My name is Stephen
I am a parent
Education is secondary 10-12

Hi Stephen,

I am going to assume that you have a regular octagon as in the diagram. I have called the side length a. Since the perimeter is 1,000 meters, a = 1,000/8 = 125 meters.

I have cut the octagon into 9 pieces, a square of area a2, four rectangles, each of area ab and 4 triangles. All that remains is to determine b. But triangle PQR is a right triangle so the theorem of Pythagoras tells us that b2 + b2 = a2.


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