Question

An equilateral triangle, having each side as a , has its corners cut away so as to form a regular hexagon. The area of the hexagon is
a.3 2 6
b.2 3 2 3
c.3 2 12
d.3 2

Answer 1

Area of regular hexagon formed after cutting away corners of equilateral triangle of side 'a' -

• A regular hexagon is formed after cutting away corners such that each the length of each side of hexagon becomes a/3. (Draw figure if necessary)
• Area of regular hexagon = 3√3/2 × (side)²
• Area = 3√3/2 × (a/3)²
• Area = √3/6 a² = a²/2√3

Answer 2

Complete question:

An equilateral triangle having each side of 6 cm has its corners cut off to form a regular hexagon. The area of the hexagon is

a. 3√3

b. 3√6

c. 6√3

d. (5√3)/2

Answer:

The area of the hexagon is c. 6√3

Step-by-step explanation:

The area of equilateral triangle is given by the formula:

Ae = √3/4 a² = √3/4 × 6² = √3/4 × 36 = 9√3 cm

The area of a corner is given by the formula:

Ac = √3/4 a² = √3/4 × 2² = √3/4 × 4 = √3 cm

Now, the area of the hexagon is:

Ah = 9√3 - 3√3 = 6√3 cm²