Question

A piece of art is in the shape of an equilateral triangle with sides of 6 in. Find the area of the piece of art. Round your answer to the nearest tenth.

Answer 1

Answer:

15.6 inches squared.

Step-by-step explanation:

According to the diagram below, the formula for the area of an equilateral triangle is the square root of 3 times the side length squared divided by 4.

The side length is 6. So, the area of the triangle is...

$\frac{\sqrt{3} * 6^2}{4}$

= $\frac{6^2 * \sqrt{3}}{4}$

= $\frac{36\sqrt{3}}{4}$

= $9\sqrt{3}$

= 9 * 1.732050808

= 15.58845727, which is about 15.6 inches squared.

Hope this helps!

Answer 2

Answer:

15.6

Step-by-step explanation:

We can take this equilateral triangle and split it in half to form a 30-60-90 triangle. This will have base of 3, and height of 3$\sqrt{3}$. The area of this is

1/2 ( 3 )( 3$\sqrt{3}$ ), but the 1/2 cancels since we have 2 halves of the triangle, and so the area is 9.

$\sqrt{3}$ is approx. 1.732, so multiplying this by 9, our answer is 15.6