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# A regular octagon ABCDEFGH has sides of length two. Find the area of t

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Math Expert
Joined: 02 Sep 2009
Posts: 54372
A regular octagon ABCDEFGH has sides of length two. Find the area of t  [#permalink]

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19 Mar 2019, 01:21
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Difficulty:

45% (medium)

Question Stats:

67% (02:14) correct 33% (04:23) wrong based on 9 sessions

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A regular octagon ABCDEFGH has sides of length two. Find the area of triangle ADG.

(A) $$4 + 2\sqrt{2}$$

(B) $$6 + \sqrt{2}$$

(C) $$4 + 3\sqrt{2}$$

(D) $$3 + 4\sqrt{2}$$

(E) $$8 + \sqrt{2}$$

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Re: A regular octagon ABCDEFGH has sides of length two. Find the area of t  [#permalink]

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19 Mar 2019, 10:56
Bunuel wrote:
A regular octagon ABCDEFGH has sides of length two. Find the area of triangle ADG.
(A) $$4 + 2\sqrt{2}$$
(B) $$6 + \sqrt{2}$$
(C) $$4 + 3\sqrt{2}$$
(D) $$3 + 4\sqrt{2}$$
(E) $$8 + \sqrt{2}$$

for the small corner triangles, it is a 45:45:90, so the side ration is $$1:1:\sqrt{2}$$
as the hypotenuse = 2, so the other sides = $$\sqrt{2}$$ each

height = $$2 + \sqrt{2}$$
base = $$2 + 2\sqrt{2}$$

so area = $$\frac{b*h}{2}$$ =$$4 + 3\sqrt{2}$$

so C IMO
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Re: A regular octagon ABCDEFGH has sides of length two. Find the area of t   [#permalink] 19 Mar 2019, 10:56
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