SOLUTION: XYZ is an equileteral triangle of length 10cm. Find: a) calculate the height if the triangle using pythagoras theorem. b) calculate the area of the triangle

Algebra ->  Triangles -> SOLUTION: XYZ is an equileteral triangle of length 10cm. Find: a) calculate the height if the triangle using pythagoras theorem. b) calculate the area of the triangle      Log On


   

Question 749006: XYZ is an equileteral triangle of length 10cm. Find:
a) calculate the height if the triangle using pythagoras theorem.
b) calculate the area of the triangle
Answer by timvanswearingen(106) About Me  (Show Source):
You can put this solution on YOUR website!
The height would be drawn from a vertex to the midpoint of the opposite side. Setting up a right triangle and using the Pythagorean Theorem:
a%5E2%2Bb%5E2=c%5E2
a%5E2%2B5%5E2=10%5E2
a%5E2%2B25=100
a%5E2=75
a+=+sqrt%2875%29
a+=+sqrt%2825%29%2Asqrt%283%29
a+=+5%2Asqrt%283%29
The height is:
5%2Asqrt%283%29cm
Area is 1/2*base*height. The base is 10 and we just found the height:
A=1%2F2%2A10cm%2A5%2Asqrt%283%29
A=5%2A5cm%2Asqrt%283%29cm
A=25%2Asqrt%283%29+cm%5E2