What is the area of the trapezoid shown?
First let's draw two lines perpendicular to the base, forming two right triangles, like this...
Now we can find h and x .
sin 60° = h / 2 so h = 2 sin 60° = √3
cos 60° = x / 2 so x = 2 cos 60° = 1
So...
the height of the trapezoid = √3 ,
the first base = 2 , and
the second base = 2 + 1 + 1 = 4
area of trapezoid = (first base + second base)/2 * height
area of trapezoid = (2 + 4)/2 * √3
area of trapezoid = 3√3 sq. units
First let's draw two lines perpendicular to the base, forming two right triangles, like this...
Now we can find h and x .
sin 60° = h / 2 so h = 2 sin 60° = √3
cos 60° = x / 2 so x = 2 cos 60° = 1
So...
the height of the trapezoid = √3 ,
the first base = 2 , and
the second base = 2 + 1 + 1 = 4
area of trapezoid = (first base + second base)/2 * height
area of trapezoid = (2 + 4)/2 * √3
area of trapezoid = 3√3 sq. units