Amy S.

asked • 06/10/16

Equilateral triangle

An equilateral triangle DEF has sides of x cm and height h cm. show that the area of ΔDEF is
((√3)/4)x^2 cm^2
 
Please show the full working. 

1 Expert Answer

By:

Mark M. answered • 06/10/16

Mathematics Teacher - NCLB Highly Qualified

Amy S.

How do you know that the height is x2√3/2?
 
Report

06/10/16

Amy S.

I mean x√3/2
Report

06/10/16

Mark M.

tutor
In a 30-60-90 triangle, the side opposite the 30° angle is one-half of the hypotenuse.
The side opposite the 60° is √3/2 of the hypotenuse.
Report

06/10/16

Amy S.

If you don't mind, could you show me your full working?
Report

06/10/16

Mark M.

tutor
Draw and equilateral triangle. Label each side "x."
Draw an altitude from the base to the opposite vertex. Label it "a."
You now have two triangles each a 30-60-90 triangle.
The side "x" is the hypotenuse. One-half of the base is the short leg.
The altitude is the long leg.
By Pythagoras:
x2 = (x/2)2 + a2
x2 = x2/4 + a2
x2 - x2/4 = a2
3x2/4 = a2
x√3 / 2 = a
Report

06/10/16

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.