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Janet is designing a garden in her backyard that is a regular octagon with a side length of 6 ft and an apothem of 7.24
ft. What is the approximate area of the garden?
O 72 ft2

O 347.5 ft2

O 173.8 ft2

O 86.9 ft2

Sagot :

fieryanswererft

Answer:

c. [tex]\sf area \ of \ octagon = 173.82 \ ft^2[/tex]

Explanation:

[tex]\sf area \ of \ octagon = 2(1+\sqrt{2} )a^2[/tex]

Here "a" refers to side length.

using this formula:

[tex]\hookrightarrow \sf area \ of \ octagon = 2(1+\sqrt{2} )(6)^2[/tex]

[tex]\hookrightarrow \sf area \ of \ octagon = 173.82 \ ft^2[/tex]

Solution:

It should be noted:

  • Area of regular octagon: 2(1 + √2)x² (x = side)

Substitute the side length into the formula.

  • 2(1 + √2)x²
  • => 2(1 + √2) × 6²

Simplify the distributive property.

  • => 2(1 + √2)36
  • => 72(1 + √2)
  • => 72 + 72√2

Simplify 72√2 using a calculator.

  • => 72 + 101.82

Add if needed.

  • => 173.82 ft²

Looking at the options, it is said that option C is correct as 173.8 and 173.82 are approximate numbers.

Option C is correct.

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