Suppose you know the perimeter and the height of an equilateral triangle. Explain how you would find the area of the triangle.
Please help me
The height of an equilateral triangle is a function of its perimeter.
So you don't need both pieces of information, as a matter of fact, they
could contradict each other
suppose you know that the perimeter is 6x units, (2x on each side)
then the height is:
h/x = tan60
h = xtan60 = √3x
area = (1/2)(base)(height) = (1/2)(2x)(√3x)
= √3 x^2
@Mrs sue
Ms Sue was one of our most respected tutors here for many years.
Unfortunately, she passed away last December and we all miss her.
Out of respect for her, I would ask you to pick another name for your ID
To find the area of an equilateral triangle when you know its perimeter and height, you can follow these steps:
1. Recall that an equilateral triangle has all three sides equal in length.
2. Since you know the perimeter of the triangle, which is the sum of all three sides, divide the perimeter by 3 to find the length of one side. Let's call this value 's'.
s = (perimeter) / 3
3. Next, use the height of the triangle to find the length of the base. In an equilateral triangle, the height bisects the base, forming two congruent right triangles.
So, using the Pythagorean theorem, the length of the base (b) is given by:
b = sqrt(s^2 - (h^2)), where h is the height.
4. Now that you have the length of the base, you can calculate the area of the equilateral triangle (A) using the formula:
A = (1/2) * b * h, where b is the base length and h is the height.
Let's summarize the steps:
1. Calculate the length of one side by dividing the perimeter by 3: s = (perimeter) / 3.
2. Calculate the length of the base using the height: b = sqrt(s^2 - (h^2)).
3. Finally, calculate the area of the equilateral triangle using the base and height: A = (1/2) * b * h.