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.

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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

step-by-step explanation: