SOLUTION: An equilateral triangle has perimeter 27 cm. what is its area?

Question 800094: An equilateral triangle has perimeter 27 cm. what is its area?

Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
an equilateral triangle with a perimeter
of 27 cm will have 3 sides = 9cm.
A line drawn from the midpoint of the
triangles base up to the highest apex
will construct a right angled triangle
of base = 4.5 cm and hypotenuse = 9 cm
The vertical side^2 = hypotenuse^2 - base^2
Vertical side^2 = 9^2 - 4.5^2
Vertical side^2 = 81 - 20.25
Vertical side =
Vertical side = 7.8 cm
Area of equilateral = 1/2(base * height)
Area of equilateral = 1/2(9 * 7.8)
Area = 35.1 cm^2
Hope this helps.
:-)
RELATED QUESTIONS
An equilateral triangle has 27 cm. What is its area? Thank... (answered by josgarithmetic,ikleyn)

Given that the area of an equilateral triangle is 153 cm^2, find its... (answered by lazi)

Given that the area of an equilateral triangle is 57 cm^2, find its perimeter. (answered by anantha)

Given that the area of an equilateral triangle is 316 "cm"^2, find its... (answered by swincher4391)

Height of an equilateral triangle is 5root 3 cm .find its area &... (answered by ikleyn)

A square whose area is 81 has its perimeter equal to the perimeter of an equilateral... (answered by josgarithmetic,MathTherapy)

What is the exact perimeter of an equilateral triangle that has a height of 18... (answered by MathLover1)

If an area of a equilateral triangle is 112cm^2, what is its... (answered by richwmiller)

Area of a equilateral triangle is 24 root 3 cm square . Then what will be its perimeter... (answered by harpazo)