Asked by Missmoo
For math, I have to find the area of a hexagon when all I know is that each side equals x. I also know that I have to use 3 thereoms. HELPP!
Answers
Answered by
Reiny
make a sketch.
from the centre draw lines to each of the 6 vertices. This will give you six equilateral triangles with sides x.
Let's concentrate on one of these
Drawing a height "h" in one of these triangles will give us a right-angled triangle of base x/2, height of h, and hypotenuse of x
so (x/2)^2 + h^2 = x^2
x^2/4 + h^2 = x^2
.
.
h = (√3/2)x
so the area of one triangle = (1/2)(x)√3/2)x
= (√3/4)x^2
but we have 6 of these, so
total area
= 6((√3/4)x^2)
= (3√3/4)x^2
from the centre draw lines to each of the 6 vertices. This will give you six equilateral triangles with sides x.
Let's concentrate on one of these
Drawing a height "h" in one of these triangles will give us a right-angled triangle of base x/2, height of h, and hypotenuse of x
so (x/2)^2 + h^2 = x^2
x^2/4 + h^2 = x^2
.
.
h = (√3/2)x
so the area of one triangle = (1/2)(x)√3/2)x
= (√3/4)x^2
but we have 6 of these, so
total area
= 6((√3/4)x^2)
= (3√3/4)x^2
Answered by
Reiny
messed up the last, line should say
(3√3/2)x^2
(3√3/2)x^2
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.