what is the area of a equalateral triangle with a peremeter of 10 units?

Answer 1

The area of an equilateral triangle is
A = (1/4)sqrt(3) * a^2, where a is the length of the side.
Since the triangle is equilateral, you know that the length of each side is 10/3.
The area is
A = (1/4)sqrt(3) (10/3)^2
A = (1/4)sqrt(3) (100/9)
A = (25/9)sqrt(3)

Answer 2

Unfortunately, unless I misunderstand, math teacher for 35 years is wrong. I see one or two correct answers, but here's how I do it (with no sines or cosines - but they would make it easier):
Equilateral = each side is 10/3
Draw a perpendicular from one side up to a vertex. That line is the "height" of the triangle. Take a look at it. Notice that you can now make a rectangle by taking one of the triangles you made and fitting it against the other so now instead of _|_ you have |_|
(sorry I can't draw the two hypotenuses of the triangles or the top of the rectangle). In other words half of one side is the rectangles base. And its height can be calculated (by trigonometry but I promised ..) by Pythagorean Theorem:
(10/3)^2 = (5/3)^2 + h^2
or h^2 = (10/3)^2 - (5/3)^2 = 100/9 - 25/9 =75/9
or h= sqrt(75/9) = sqrt(3*25/9) = 5/3*sqrt(3)
and b= 5/3 so A=bh = 5/3*5/3*sqrt(3) = 25/9*sqrt(3) or ~4.81

Answer 3

Hi. 10 divided by 3 is the length of each side. A line drawn vertical through the apex divides the triangle in half. The base leg is ('10/3' /2) and the opposite angle is 30 (60/2). Use this to solve for a right triangle using sin = opp/hyp or (sin 30 = (10/3 /2) / 10/3. Multiply the result by 2 (for both halves of the triangle).Does this help?

Answer 4

In a equalateral all the sides are squal so if the perimter is equal to 10 units each side is then equal to 10 / 3 = 3.33 therefore the formula for a triangle , any triangle , is equal to 1/2 bh ( 1/2 of the base "times" the height
so 3.33 x 3.33 = 11.0889 / 2 = 5.5445 the sres = 5.5445 units

Answer 5

draw out the triangle. divide 10 by 3 because it is equi. take one of the sides and divide it into half. So now u have 1.5 and 1.5. We need the height. Since equilateral triangle has same angles, so all three would be 60 degrees. So we now have a 30 60 triangle, with 60 being the theta angle and 1.5 is ur adjacent side. We can either use tangent to find out, or just use the 30-60 triangle theorem. triangle theorem is so much quicker, so ur height would now become 1.5sqrt3. Multiply that by ur base, 3, divide the product by 2, and theres ur area.

Answer 6

S=sqrt(p*(p-a)*(p-b)*(p-c)) for any triangle with sides a, b & c, p=(a+b+c)/2 & =10/2. As a=b=c, then 5=(3/2)*a or a=10/3,
and S=sqrt(5*(5-10/3)^3)=
=sqrt(5*(5/3)^3)=
=(25/9)*sqrt(3) - hi Lucas!

Answer 7

when the perimeter is 10 so this emans that each side has 103 units

the A of eq. triangle is = side^2 times squareroot of 3 over 4

so (10/3)squareroot of 3 all over 4

100 squareroot of 3 all over 36 simplify
25 squareroot of 3 over 4 units^2

Answer 8

A = bh/2
b= 10/3
h = (1/3)√(10^2 - 5^2) = 5√2^2 - 1) = (5/3)√3
A = (1/2)(10/3)*(5/3)√3
A = (25/9)√3 sq. units
A ≈ 4.8112 sq. units

Answer 9

You need more information to answer this question such as the height or base of the triangle. Otherwise the area will differ.

Answer 10

just a second