Find the area of the equilateral triangle whose sides are 4yd.?

Answer 1

Simple way of getting area of an equilateral triangle :

In trigonometry, you have the formula 1/2( AB * AC *sin(A) )

In an equilateral triangle, we know AB = AC and Angle A = 60 degrees.

Hence the area is simply,

1/2 * 4 * 4 * root(3)/2 = 4root(3) = 6.92 yds

Answer 2

ANS: 4 yards square

Two ways to do this:
1, imagine you had four of the same triangles and you arranged them into a square .. each side of the square would be 4yds, making the area 4*4 which is 16yards sqaure .. but you only want one of the 4, so divide 16/4 ... ans:4

2, draw a line from any point bisecting the opposite line, there is now a 90 degree angle and the untouched 4yd side is the hypoteneuse, as the line (becuase it is equilateral triangle) bisects the 4 into 2, we know have a hypo of 4 and one leg of two
a^2 = b^2 +c^2 shows us that the line we draw from one point measures 2yds
Area = 1/2b*H
1/2 *2 *4 = 4

Answer 3

Area = 1/2 L x H

L = 4

The trick here is finding the height. If you draw the height of the triangle into a diagram of this equilateral triange, you will see that the picture looks like two tall triangles touching at the middle. Both of these triangles are 60-30 rigth triangles with an hypotenuse of 4, one of the legs with a length of 2, and the last one (the height) unknown. Doing a little Pythagoras work, the height can be calculated to be 2*SQRT(3).

So, plugging this into your formula:

A = 1/2 * 4 * 2*SQRT(3) = 4*SQRT(3)