Question

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

Answer 1

Answer:

c. $\sf area \ of \ octagon = 173.82 \ ft^2$

Explanation:

$\sf area \ of \ octagon = 2(1+\sqrt{2} )a^2$

Here "a" refers to side length.

using this formula:

$\hookrightarrow \sf area \ of \ octagon = 2(1+\sqrt{2} )(6)^2$

$\hookrightarrow \sf area \ of \ octagon = 173.82 \ ft^2$

Answer 2

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.