Question

from a square with sides of length 5 triangular pieces from four corners are removed to form a regular octagon find the area he moved to the nearest integer

Answer 1

Answer:

4

Step-by-step explanation:

four corners are removed to form a regular octagon

Let say Equal Sides of Triangle cut = b

Then side of Hexagon = 5 - 2b

Side of Hexagon = √b² + b² = b√2

5 - 2b = b√2

=> b(2 + √2) = 5

=> b = 5/(2 + √2)

Area of Triangle = (1/2)b * b = (1/2)  25/(4 + 2 + 4√2)   = 25/(12 + 8√2)

Area of 4 Triangles = 25/(3 + 2√2)

= 25(3 - 2√2)/(9 - 8)

= 25 ( 3 - 2√2)

= 4.3

= 4  (to the nearest integer)