Question

A piece of art is in the shape of an equilateral triangle with sides of 25in. Find the area of the piece of art. Round your answer to the nearest tenth. Answers: A:221in^2 B:270in^2 C: 541.3in^2 and D: none of these

Answer 1

A=$\sqrt{3}/4$ * side length^2
A=270.663
The answer is B.

Answer 2

To find the area of a triangle you need the formula (base*height)/2.  We know the base is 25in however we need to find the height to have everything for the formula. If you draw a picture of this equilateral triangle so the bottom is a flat side, the height goes straight up the middle, splitting the triangle into two equal pieces.  However, to find the height, you have to use Pythagoras's theorem (a^2+b^2=c^2).  c is the hypotenuse so that is the 25in, a is half the width of the base, 12.5in, and b is what you are looking for.  When solved, b becomes about 21.65, or if you have to be exact- sqrt{468.75}.  Then plug this in for the height in the original equation.
(25*sqrt{468.75})/2≈270.63 in^2