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The area of a regular octagon is 35 cm2. What is the area of a regular octagon with sides five times as long?

A. 625 cm2

B. 875 cm2

C. 175 cm2

D. 245 cm2

Respuesta :

W0lf93
The answer is B. 875 cm2. This is calculated by taking 35 * 5 * 5. The relationships between areas and side lengths of similar shapes is a squared relationship. Since the answer wanted 5 times, we do 5 times 5 and multiply that by our current area.

Answer with Step-by-step explanation:

Area of octagon=2(1+√2)a²

Where a is the length of the side of the octagon

Area=35 cm²

Let a' be the length of side of new octagon

a'=5a

Area=2(1+√2)a'²

       =25×2(1+√2)a²

       =25×35 cm²

       = 875 cm²

Hence, correct option is:

B. 875 cm²

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