What is the side of an equilateral triangle if its area is root 243/4 sq cm.

Good question.

The area of a triangle is the base times the height.

A=b * h, where A is the area, b is the length of the base, and h is the height.

So what three sets of numbers multiply to 24.

To do this, we can factor 24, starting from 1 going up to approximately the square root of 24, which is 5. After this, the numbers will just reverse.

1 * 24
2 * 12
3 * 8
4 * 6

Pick any three of these and make triangles with the base being one number, and the height being the other number. Then connect the ends of the line to the top of the height line. You can move the height along the base and create many many different triangles with an area of 24 cm squared.

Good luck,

Paul

I assume the length of a side is 16 in, and the height of the prism is 23 inches.
Volume of a prism is V_prism=(Area of base)*(height of prism)
Area of base is made up of the area of the 6 equilateral triangles with sides =16 inches. The height of such triangles is given by 8*SQRT(3).
Use the Pythagorean theorem or the trigonometric ratios to find the height of each of the 6 traingles.
Area of base =6*16*(8*SQRT(3))/2 sq in
Volume =6*8*8*23*SQRT(3) cubic inches
Calculate the value in cubic inches and convert to gallons: I leave that task to you.

Calculate the area of the base (you need the measure of the side) in sq. inches and multiply by the height.

Solve the resulting quadratic equation
2X^2+3X-90=0
Discriminant: (3)^2-4(2)(-90)=729=(27)^2
Two roots
X_1=(1/4)*(-3+27)=6
X-2=(1/4)*(-3-27) =-(15/2), negative
Since the width must be positive, reject the negative root and keep X_1=6
Width =6
Length=2(6)+3=15
Check 6*(15)=90. Checks OK

A contradiction is what. An equilateral triangle has 3 equal sides, and therefore equal angles. An isosceles triangle has 2 equal sides and one shorter or longer..

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You need to calculate the slant height of the pyramid for the formula of the lateral area. You should find a value of (1/2)*SQRT(203) or about 7.1239 cm



You need to calculate the altitude (height) of the pyramid from the apex (summit) to the center of the base triangle (center of inscribed circle, barycenter, orthocenter). The hypotenuse of such triangle is the slant height. One leg is the altitude (to be found), the measure of the second leg is (1/3) the altitude of the equilateral triangle that forms the base. You should find (1/3) m MH= (1/3)* (11/2)*SQRT(3)


1. Calculate the area of the base (use a formula for the equilateral triangle or the general formula for a triangle: you have its height MH ).
2. Lateral area = 3 times the area of triangle Triangle ECD (in yellow above).
3. Total area = area of base + lateral area.
4. Volume= (1/3)(Area of base)* (height of pyramid)
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Well, there is classification by sides, equilateral with 3 equal sides, Isosceles with two equal sides, and scalene with no equal sides, but you talk about angles, but I wanted to point out equilaterals have 3 equal angles, isoceles have 2 equal angles and scalene have no equal angles.
So, now we talk about angles: a Right trianlge has one angle that is 90 degrees, an Obtuse triangle has one angle greater than 90 degrees, and an Acute has no angles over 90 degrees.
Thus, it is possible to have a (scalene or isoceles) AND (acute, obtuse, or right) triangle, but never an equilateral AND (obtuse or right). The angles can't be equal and 90+ degrees if all three must equal 180 degrees.

Well, just multiply 7.5 by 3. Solution: 22.5

Yes, there is shortcut because this is right triangle, so you can use Pythagorean theorem (see picture).

1. Length of hypotenuse is square root of sum of squares of lengths of other two sides of triangle, which is equal to square root of 30^2+10^2=31.6 cm.
2. Sin(a)=longer cathetus/hypotenuse=0.949 so a=arcsin(0.949)=71.6 degrees
3. Finally b=90-a=18.4 degrees.

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Hi nanaeden

Use the formula depending on what is given
If one side and vertical height from that side to the opposite vertex is given, use the formula 1/2 of basexheight
If 3 sides of the triangle are given use the formula
sq root of [ s(s-a)(s-b)(s-c)] where a,b, c are the 3 sides and s is semi- perimeter.
Familiarise with formulae to solve Maths problems.
If it is helpful, please give a rating.
Have a nice day
luciana44