Question

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

Answer 1

Answer:

the 4 pieces removed are of equilateral triangles of side each 5/3 unit

area of 4 equilateral triangles: 4xv3/4 (5/3)^2 = 4x1.732x25/4x9

4.8 unit or 5 unit appr.

Answer 2

Answer:

4

Step-by-step explanation:

From a square with sides of length 5, triangular pieces from the four corners are removed to form a regular octagon. Find the area removed to the nearest integer?

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)