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What is the height of an equalateral traiangle with sides of 10 cm long what about for any equalateral triangle will the height always be the same as one of the sides?
Wiki User
∙ 11y ago
8.66cm; no
If you have heard of a 30-60-90 triangle with sides in the ratio of 1 to sqrt(3) to 2, then this should be easy:
Draw an equilateral triangle with one side at the bottom. Find the middle of the base, and draw a vertical line to divide the triangle in two. (Sorry, I can't draw this!) Now suppose the length of each side of the equilateral triangle is 2 units. You have divided the base into two parts each with a length of 1.
Each smaller triangle is a right triangle with hypotenuse 2 and one side 1 unit long. the 3rd side is the altitude of the equilateral triangle, call it h. Pythagoras tells us that 12 + h2 = 22 <=> 1 + h2 = 4 <=> h2 = 4-1 = 3 <=> h = sqrt(3).
The height of an equilateral triangle is always sqrt(3) times half the length of a side. This comes out to about 0.866 times the length of a side, so if the side is 10cm long, the height will be 8.66cm.
(The height isn't the same as one of the sides, it's about 13/15 of it.)
Wiki User
∙ 11y ago
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How many altitudes can a traiangle have?
A triangle only has one altitude which is its perpendicular height.
What is the perimeter and area of a equalateral triangle whoose base 6m and height is 4m?
This is not an equilateral triangle if height is 4 m the base is 6 m and by Pythagorean theorem the other sides are 5 m perimeter is 6 + 5 + 5 = 16m Area = base x height = 6 x 4 = 24 sq m
How do you find the side of an equilateral triangle whose area is 36 radical 3?
Suppose the sides of the triangle are 2x. Drop a perpendicular bisector from the apex to the base. Now consider the half-triangle formed. The hypotenuse is one of the sides of the original triangle, so 2x in length. The base is half the side of the original traiangle, so x in length. So, by Pythagoras, the height2 is (2x)2 - x2 = 3*x2 So height = x*sqrt(3) Then area of the whole traiangle = base*height/2 = 2x*x*sqrt(3)/2 =x2*sqrt(3) This is given as 36*radical 3 so x2 = 36 ie x = 6 So the sides, = 2x = 12 units.
How many people do you need to form a solid equalateral triangle then go into a square?
If these people are relatively equal in height, lying down and viewed from above, then the following may be your answer: The least number of people you can use to create an equalateral triangle, is THREE. The least number of people you can use to create a square, is FOUR. Therefore, you will need to use a number that has both 3 and 4 as a factor. EX - 12, 24, 36, 48, etc
Which is bigger a pyramids height or its slant height?
Its slant height is bigger. Think of it as a triangle: the hypotenuse is always the largest side, and the slant height is like the hypotenuse.
How many altitudes can a traiangle have?
A triangle only has one altitude which is its perpendicular height.
What triangle uses half of base times height?
Equalateral
How do you find the height of an equalateral triangle?
To find the altitude or height of an equilateral triangle, take one-half of the length of a side of the triangle and multiple by "square root" of 3. So, if for example, the side has length 10, the height = 5 Square root of 3.
What is the perimeter and area of a equalateral triangle whoose base 6m and height is 4m?
This is not an equilateral triangle if height is 4 m the base is 6 m and by Pythagorean theorem the other sides are 5 m perimeter is 6 + 5 + 5 = 16m Area = base x height = 6 x 4 = 24 sq m
How do you find the area of an equalateral triangle?
Do you mean an equilateral triangle? Then if so then the formula for the area of any triangle: 0.5*a*b*sinC whereas a and b are the embraced sides of angle C And in the case of an equilateral triangle it is: 0.5*any side squared*sin(60 degrees) Alternatively use Pythagoras' theorem to find the altitude of the triangle then use: 0.5*base*height = area
How do you calculate the height of an equalateral triangle given the length of one side and all three angles?
Let a be the length of the side. If we draw the height (altitude) of the equilateral triangle which also is a median, then the one half of the side is a/2. From the Pythagorean theorem, h = √[(a^2 - (a/2)^2] = √(a^2 - a^2/4) = √[(3a^2)/4] = (a/2)√ 3
How do you find the side of an equilateral triangle whose area is 36 radical 3?
Suppose the sides of the triangle are 2x. Drop a perpendicular bisector from the apex to the base. Now consider the half-triangle formed. The hypotenuse is one of the sides of the original triangle, so 2x in length. The base is half the side of the original traiangle, so x in length. So, by Pythagoras, the height2 is (2x)2 - x2 = 3*x2 So height = x*sqrt(3) Then area of the whole traiangle = base*height/2 = 2x*x*sqrt(3)/2 =x2*sqrt(3) This is given as 36*radical 3 so x2 = 36 ie x = 6 So the sides, = 2x = 12 units.
How many people do you need to form a solid equalateral triangle then go into a square?
If these people are relatively equal in height, lying down and viewed from above, then the following may be your answer: The least number of people you can use to create an equalateral triangle, is THREE. The least number of people you can use to create a square, is FOUR. Therefore, you will need to use a number that has both 3 and 4 as a factor. EX - 12, 24, 36, 48, etc
Does an acute triangle always have the smaller area than an obtuse triangle?
No reason why it should, area varies as base and height.
Is slant height greater than the height?
Its slant height is bigger. Think of it as a triangle: the hypotenuse is always the largest side, and the slant height is like the hypotenuse.
Which is bigger a pyramids height or its slant height?
Its slant height is bigger. Think of it as a triangle: the hypotenuse is always the largest side, and the slant height is like the hypotenuse.
What is the relationship between the area of a parallelogram and a triangle when the base and height are the same?
The area of a parallelogram is base x height and the area of a triangle is 1/2 x base x height. So the area of a parallelogram will always be 2 times bigger than a triangle with the same base and height.
