Question

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The hexagonal seating section in an auditorium has a small entrance at the front. A walkway leading from the entrance to the front of the stage is
30 ft long. What is the approximate area of the entrance and seating section combined?
30 ft
Each side of the hexagon is about oft long. The area of the seating section is about
ft². The area of the entrance and seating section combines is about
ft².
ft². The area of the entrance is about

Answer 1

Each side of the hexagon is about 105.219 ft².

• The area of the seating section is about 631.315 ft².
• The area of the entrance and seating section combines is about 46.764ft².
• The area of the entrance is about 678. 078ft².

What is the hexagon about?

Note that:

A F: 30 ft long.

A O = 1/2 A F = 3ft

Δ C J X =  0 X = 1/2 (A F - A O)

= 1/2 (30-3)

= 13.5ft

Sin 60° =$\frac{0x}{cx}$

cx = $\frac{ox}{sn 60}$

= 15.558ft = CJ (Sides)

Hence: Each side of the hexagon is: 1/2 CJ  x OX  = 105.219 ft².

The area of the seating section is:

6 ( Each side of the hexagon )

=  6 x 105.219 ft².

631.315 ft².

The area of the entrance and seating section combines is:

CJ x AO = 46.764ft².

The area of the entrance is:

631.315 ft²+ 46.764ft².

= 678. 078ft².

Hence, Each side of the hexagon is about 105.219 ft².

• The area of the seating section is about 631.315 ft².
• The area of the entrance and seating section combines is about 46.764ft².
• The area of the entrance is about 678. 078ft².

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