Question

Hello there ^ _ ^ I would like you to do me a favor and help me with this question. Thanks!

Answer 1

Hello Gary!

1. A hexagon is made up of six triangles. So to get its area, you need to take the area of one triangle and multiply it by 6.

2. You already have the base. The height of an equilateral triangle = base/ 2 * √(3) That will give you the height. The area of a triangle is A=bh/2 You know b is 4, and that formula will give you h.

3. 4/(23–√) Or multiply by the reciprocal, 43–√/2

4. Area of triangle = b*h/2 = 4* (4√(3)/2) / 2 = 4√(3) Area of hexagon = 6 * area of triangle = 6 * 4√(3) = 24 √(3)

5. The area of one triangle is 43-√. You need to multiply this times 6 to get the whole hexagon. So 6∗(43–√)=243–√.


Hope this Helps! Have A Wonderful Day! :)

Answer 2

As it is just 6 equilateral triangles and the formula for area of a triangle 
1/2 * base * height
and you can find the height by using pythagoras c^2 - b^2 = a^2 
so do 4^2 - 2^2 = 16 - 4 = 12
6 * 1/2 * 4 * $\sqrt{12}$ = $12 \sqrt{12} = 24 \sqrt{3}$