Question

The area of the regular octagon is 10.15 cm2.
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

Answer 1

Answer:

1.75 cm

Step-by-step explanation:

Area of the octagon = A = 2(1+√2) a

where 'a' = Side of the octagon.

∴ 10.15 = 2(1+√2) a²

∴ a² = 10.15 ÷ [2×(1+1.414)]

∴ a² = 10.15 ÷ 4.828

∴ a² = 2.102

∴ a = 1.45 cm

Area of the octagon can also be calculated as

A = 8 × (a × h)/2

... considering 8 triangles with

base = a = face of octagon

Height = h = Apothem of octagon

∴ 10.15 = 8 × (1.45 × h)/2

∴ h = 10.15 ÷4 ÷ 1.45

∴ H = 1.75  cm

∴ Apothem of octagon = 1.75 cm

Answer 2

The correct answer is:

B. 1.75 cm

The measure of the apothem, rounded to the nearest hundredth of a centimeter is 1.75 cm.

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