Question

The triangle is an equilateral triangle

One side is A

The radius is A/2

What is the area of the center triangle?

Answer 1

Answer:

$Orange\ area = A^2(\sqrt{3}/4 - \pi/8) = 0.0403A^2$

Step-by-step explanation:

First let's find the area of the triangle, using the formula:

$Area\_triangle = side^2\sqrt{3}/4$

$Area\_triangle = A^2\sqrt{3}/4$

Now, let's find the area of each circular sector of 60° (internal angle of a equilateral triangle):

$Area\_sector = \pi*radius^2*60/360$

$Area\_sector = \pi*(A/2)^2/6$

$Area\_sector = \pi*A^2/24$

Now, To calculate the orange area in the center, we have:

$Orange\ area = Area\_triangle - 3*Area\_sector$

$Orange\ area = A^2\sqrt{3}/4 - \pi*A^2/8$

$Orange\ area = A^2(\sqrt{3}/4 - \pi/8)$

$Orange\ area = 0.0403A^2$