Given a regular triangle with a side of 12 cm. Find: a) height; b) area;

Given a regular triangle with a side of 12 cm. Find: a) height; b) area; c) the radius of the inscribed circle; d) the radius of the circumscribed circle.

a)

The height in such a triangle divides the side in half, then half is equal to:

12: 2 = 6.

Now we will find the height – leg in a right-angled triangle:

√ (122 – 62) = √ (18 * 6) = 6√3.

Answer: 6√3 cm.

b)

Let’s determine what the area will be equal to in our case:

1/2 * 12 * 6√3 = 36√3.

Answer: 36√3 cm2.

v)

Let’s determine what the radius of the circle will be equal to, which is inscribed in it:

r = a / 2√3;

12: 2√3 = 2√3.

Answer: 2-3 cm.

G)

Let’s define what is the radius of the circle that is described around it:

R = a / √3;

12: √3 = 4√3.

Answer: 4√3 cm.