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

15.6 inches squared.

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...

`(√(3) * 6^2)/(4)`

=
`(6^2 * √(3))/(4)`

=
`(36√(3))/(4)`

=
`9√(3)`

= 9 * 1.732050808

= 15.58845727, which is about 15.6 inches squared.

Hope this helps!

Answer 2

15.6

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
`√(3)`. The area of this is

1/2 ( 3 )( 3
`√(3)` ), but the 1/2 cancels since we have 2 halves of the triangle, and so the area is 9.

`√(3)` is approx. 1.732, so multiplying this by 9, our answer is 15.6