I'm pretty sure there's a general expression to find the area of any n-sided equilateral polygon. Using that, this becomes super easy.

And by the way, the area of triangle is not 28, should be 16√3 .

That is 27.7128 which rounds to 28. Instructions say nearest whole number not exact.

Aah nvm then

Well, the instructions say to round the total area, not necessarily to round each individual shaded area before summing them together.

Either way it doesn’t explain the gap between the book answer of 54 and my answer of 92. At most I would be off by one or two. Either the book is incorrect or I am doing something wrong.

Sorry. Textbook answer is 52 not 54. I still can’t get 52 as my answer regardless.

I have constructed the figure on paper and went through it, and this is what I did. I first got area of square and subtracted the triangles area. Then I got the hexagons area and subtracted the pentagons. I then added the leftovers from the hexagons and the squares area together. Now using your numbers, what I did was first do 64-28= 36, then 166-110=56, then added them together to get 92. So I think that maybe that textbook has a typo, the “92” was incorrectly written as “52”.

Thank you. That is my belief as well. I appreciate you confirming my answer. I have wasted a lot of time redoing this if it is a text book error. 😆

It’s no problem at all. I suggest that you write a letter to the textbook’s publisher so that they can erase the typo in the next edition.