Hi,
I need to find the length of the sides of an octagon with an area of 289 in2.
Thank you,
Andrew

 

Hi Andrew,

Divide up the octagon as in the diagram.

The octagon is then partitioned into

1 square of area s2 square inches
4 rectangles, each of area s a square inches
4 triangles, each of area a2 square inches

The sum of the areas of these 9 regions is 289 square inches so

s2 + 4 s a + 4 a2 = 289

Use Pythagoras Theorem with triangle PQR to write a as a function of s, substitute into the equation above and solve for s.

Penny