What is the area of the regular hexagon ABCDEF? Explain your reasoning.

Based on the information given the area of hexagon is 2340.

First step is to find the area of the rectangle:

Area of rectangle= (15 + 30 + 15)(26 + 26)

Area of rectangle=60×52

Area of rectangle= 3120

Second step is to find the area of the 4  triangles:

Area of rectangle =[1/2(15)(26)]×4

Area of rectangle= 195 × 4

Area of rectangle= 780

Third step is to find the area of hexagon:

Area of hexagon= 3120 - 780

Area of hexagon=2340

Inconclusion  the area of hexagon is 2340.

Learn more about area of hexagon here:link

2340 units²

Step-by-step explanation:

The easiest way to solve for the area of the hexagon is to find the area of the rectangle and subtracting the area of the triangles from it.

First, find the area of the rectangle:

A(rectangle) = (15 + 30 + 15)(26 + 26)

A(rectangle) = (60)(52)

A(rectangle) = 3120

Next, find the area of the 4 triangles:

A(triangles) = 1/2(15)(26) · 4

A(triangles) = 195 · 4

A(triangles) = 780

Finally, subtract the two areas to find the area of the hexagon:

A(hexagon) = 3120 - 780

A(hexagon) = 2340

439400

step-by-step explanation:

130^2 = 16900

16900*26 = 439400

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true