Question

Hello all!

I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.

If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.

Anyways, please show all of your work and explain your thinking! Be sure to answer both steps! Thanks!

Answer 1

A. Pentagon with side of 4 ft

Area of a polygon formula:

• A= (1/4) × n × s² × cot(π/n), where n-number of sides, s-side length

Applied to our pentagon:

• A = (1/4)×5×4²×cot(π/5) ≈ 27.5 ft²

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B. Octagon with apothem of 5 cm

Area of polygon:

• A = n × a² × tan(π/n), where n-number of sides, a- apothem

Applied to our octagon:

• A = 8×5²×tan(π/8) ≈ 82.8 cm²