Aregular hexagon has sides of 2 feet. what is the area of the hexagon?

Look at the picture.

The longer diagonals of the hexagon divide it into 6 equilateral triangles.

Method 1.

Use the Pythagorean theorem to calculate the height of triangle:

Calculate the area of the triangle:

Calculate the area of the hexagon:

Method 2:

Use the formula of the area of an equilateral triangle:

Calculate the area of the hexagon:

Method 3.

Use the trigonometric function to calculate the height of a triangle:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)