What is the area of this figure?

Geometry Level 2

What is the area of this octagon. Share your work below.


The answer is 120.

Jake Schreiner by jake schreiner , 16, USA

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2 solutions

A regular octagon is composed of 8 congruent isosceles triangles. One triangle has a base of 5 cm and a height of 6 cm. So the area of the octagon is the area of 8 triangles.

A = 8 × 1 2 × b a s e × h e i g h t = 8 × 1 2 × 5 × 6 = 120 c m 2 A = 8 \times \dfrac{1}{2}~\times~base~\times~height=8 \times \dfrac{1}{2}~\times 5~\times 6 = \boxed{120~cm^2}

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I think this answer is not correct because in a regular octagon, the height is not 12/2 but 12.70107/2. The figure here is NOT a regular hexagon, and the area is 119 (big square 12^2 = 144 - a half small square at the four vertices, i.e (5/sqrt(2))^2 x 2 = 25, 144-25=119). This can be easily checked with Geogebra.

Gerard Boileau - 2 years, 5 months ago

I am confused about what you mean. The height of one of the 8 isosceles triangles is 6, as shown in the figure. I am not sure how a regular hexagon is involved in this, and assume it is typo. A regular octagon does not have a fixed height, like I believe you have suggested as being 12.70107/2. Also, I do not know where you are getting numbers such as 119 and 144; also, I am confused to why you are squaring and square rooting numbers as there is no need to do that.

Mikael Bashir - 2 years, 2 months ago
Jake Schreiner
Apr 21, 2018

The area of the octagon is 120 units^2 because the formula for any regular polygon is 1/2 a b*# of sides.

Now let's do the math 1/2 6 5*8=120
So the answer is 120 units^2

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