The measure of the apothem, rounded to the nearest hundredth of a centimeter is 1.75cm.
Hence, option B is the correct answer.
This question is Incomplete, the complete question is:
The area of the regular octagon is 10.15cm².
What is the measure of the apothem, rounded to the nearest hundredth of a centimeter?
1.27 cm
1.75 cm
2.33 cm
2.54 cm
What is the measure of the apothem?
Note that; the area of an octagon is expressed as:
A = 2( 1 + √2 )a² = Perimeter × apothem/2
Where a is the dimension of each of its side, apothem is also height.
Given that;
- Area of the octagon A = 10.15cm²
- Length of each side a = ?
We find a.
A = 2( 1 + √2 )a²
A = 2( 1 + √2 )a²
a² = A / 2( 1 + √2 )
a² = 10.15cm² / 2( 1 + √2 )
a² = 10.15cm² / 4.8284
a² = 2.1021cm²
a = √2.1021cm²
a = 1.44986cm
Next, we determine the apothem.
Area = Perimeter × apothem/2
Area = (8 × a ) × apothem/2
10.15cm² = (8 × 1.44986cm ) × apothem/2
10.15cm² = 11.5988965cm × apothem/2
apothem/2 = 10.15cm² / 11.5988965cm
apothem/2 = 0.87508cm
apothem = 2 × 0.87508cm
apothem = 1.75cm
The measure of the apothem, rounded to the nearest hundredth of a centimeter is 1.75cm.
Hence, option B is the correct answer.
Learn more about polygons here: brainly.com/question/22408868
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