mathsurgently needed
posted by Anonymous .
ABCD is a square with length of each side 1cm. An octagon is formed by lines joining the vertices of the square to the mid points of opposite sides. Find the area of the octagon?

mathsurgently needed 
Steve
Let the corners of the square be at (0,0),(1,0),(0,1),(1,1)
y=12x intersects y=(1x)/2 at (1/3,1/3)
So, in each of 4 quadrants, the exterior of the octagon is a trapezoid and a triangle
trapezoid has area 3/16
triangle has area 1/48
sum has area 5/24
The 4 have area 5/6
The octagon thus has area 1/6
Or, consider that the octagon has
side = √5/12
apothem = 1/2√5
area = 1/2 * 8√5/12 * 1/2√5 = 1/6
Respond to this Question
Similar Questions

maths
Let ABCD be a square with side legnth 7cm. Another square KLMN is inscribed into ABCD such that its vertices lie on the sides of ABCD. Find the lenghts of parts of ABCD sides which are divided by the vertices of KLMN. If [the area … 
geometry
The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon? 
geometry
The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon? 
geometry
The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon? 
geometry
The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon? 
geometry
The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon? 
geometry
The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon? 
math
A square whose side is 2m has it's corner cut away so as to form a octagon with all sides equal find the length of each side of octagon and also find the area of the octagon? 
geometry
ABCD is a square of side length 1. E , F , G and H are the midpoints of AB , BC , CD and DA , respectively. The lines FA , AG , GB , BH , HC , CE , ED and DF determine a convex 8gon. By symmetry, this octagon has equal sides. If s … 
Maths (Proof)
An octagon is formed by joining the points (7,0), (5,5), (0,7), (5,5), (7,0), (5,5), (0,7), (5,5) and (7,0). The octagon is regular. I have used proof by exhaustion and got that all sides are square root of 29. Then sketched …