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What is the volume of a pyramid of height 10 cm when the base is an equilateral triangle with sides of length 12 cm?
The rule for the volume of a pyramid is:
V = 1/3 x Area of base x Height
So first, we'll find the area of the base.
The rule for the Area of a triangle is
A = [bcSin(theta)]/2 (you can also use A = 1/2 x base x height.. but that's slower in this case)
We know all that it is an equilateral triangle, and because a triangle must have 180 degrees all together, we know that each angle must be 60 degrees.
So now we will find the area
A = [bcSin(theta)]/2
b and c are both 7, and the angle is 60 degrees so substitute that in
A = [7x7sin(60)]/2
A = 21.218cm^2
Now we know the Area and the Height, so we can find the volume.
V = 1/3 x Area of base x Height
Substitute in our value of 21.218cm^2 for Area and 10cm for height
V = 1/3 x 21.218 x 10
V = 70.727 cm^3
What else can I help you with?
Area of equilateral triangle?
To get the area of an equilateral triangle, you just need to know the length of one side. Multiply the length of one side by the square root of three and then divide the product by four, and you will get the area of the triangle.
What is the height of an equilateral triangle with the side lengths of 8 inches?
To find the height of an equilateral triangle, you can use the formula: height = (√3/2) * side length. For an equilateral triangle with side lengths of 8 inches, the height would be (√3/2) * 8 inches, which simplifies to approximately 6.93 inches. This height represents the perpendicular distance from any vertex to the opposite side in an equilateral triangle.
The length of an equilateral triangle is 66 what it the length of one side of the triangle?
10
What is the area of an equilateral triangle of side 2a?
The height of an equilateral triangle is √3/2 x side_length. So for an equilateral triangle of side length 2a, the area is: area = 1/2 x base x height 1/2 x (2a) x (√3/2 x 2a) = √3 a2
What does equilateral triangle mean?
An equilateral triangle is one in which all three sides are of the same length.
What is the height of an equilateral triangle with a length of x?
Cutting the equilateral triangle in half results in two right triangles each with a base of length x/2, and angles of 30, 60, and 90 degrees. Using the lengths of sides of a 30-60-90 triangle it can be found that the height is (x/2)√(3), which is the same as the height of the equilateral triangle.So the height of the equilateral triangle is x√(3) / 2.
Area of equilateral triangle?
To get the area of an equilateral triangle, you just need to know the length of one side. Multiply the length of one side by the square root of three and then divide the product by four, and you will get the area of the triangle.
How do you find the height of an equilateral triangle if you have the length of the hypotenuse?
An equilateral triangle hasn't a hypotenuse; hypotenuse means the side opposite the right angle in a right triangle. An equilateral triangle has no right angles; rather all three of its angles measure 60 degrees. Knowing the length of the hypotenuse of a right triangle does not give enough information to determine the triangle's height. But the length of a side (which is the same for every side) of an equilateral triangle is enough information from which to calculate the height of that triangle. The first way is simply to use the formula that has been developed for this purpose: height = (length X sqrt(3)) / 2. But you can also use the geometry of right triangles to solve for the height. That is because you can bisect the triangle with a vertical line from the top vertex to the center of the base. The length of that line, which splits the equilateral triangle into two right triangles, is the height of the equilateral triangle. We know a lot about each right triangle formed by bisecting the equilateral triangle: * - The hypotenuse length is the length of the equilateral triangle's side. * - The base length is half the length of the hypotenuse. * - The angle opposite the hypotenuse is 90 degrees. * - The angle opposite the vertical is 60 degrees (the measure of every angle of any equilateral triangle). * - The angle opposite the base is 30 degrees (half of the bisected 60-degree angle). * - (Note that the sum of the angles does equal 180 degrees, as it must.) Now to solve for the height of a right triangle. There are a few ways. For labeling, let's let h=height of the equilateral triangle and the vertical side of the right triangle; A=every angle of the equilateral triangle (each 60o); s=side length of any side of the equilateral triangle and thus the hypotenuse of the right triangle. Since the sine of an angle of a right triangle is equal to the ratio of the opposite side divided by the hypotenuse, we can write that sin(A) = h/s. Solving for h, we get h=sin(A)/s. With trig tables you can now easily find the height.
How do you calculate height of a equilateral triangle?
square root (3) * side length / 2
What is the formula for the area for an equilateral triangle?
-- The area of any triangle is 1/2 (length of the base x height). -- For an equilateral triangle, that's equivalent to 1/2 x sqrt(3) x (length of a side).
What is the slant height of a pyramid that has all sides as equilateral triangles with sides of length of 9 cm and the surface area of the pyramid is 140.4 square cm?
The surface area of the pyramid is superfluous to calculating the slant height as the slant height is the height of the triangular side of the pyramid which can be worked out using Pythagoras on the side lengths of the equilateral triangle: side² = height² + (½side)² → height² = side² - ¼side² → height² = (1 - ¼)side² → height² = ¾side² → height = (√3)/2 side → slant height = (√3)/2 × 9cm = 4.5 × √3 cm ≈ 7.8 cm. ---------------------------- However, the surface area can be used as a check: 140.4 cm² ÷ (½ × 9 cm × 7.8 cm) = 140.4 cm² ÷ 35.1 cm² = 4 So the pyramid comprises 4 equilateral triangles - one for the base and 3 for the sides; it is a tetrahedron.
What is the base and height of an equilateral triangle with an area of 12?
The base length is 5.2643 units and the height is 4.55902 units.
A shape having the same dimensions of length height and width?
Cube, equilateral pyramid, and sphere.
A triangle with all sides the same length?
is called an equilateral triangle
What is the area of an equilateral triangle with sides of ten inches and height of seven inches?
There is a problem with your question, namely that such a triangle does not exist. An equilateral triangle with sides of length 10 would have a height of 5 * (root 3), which is approx 8.66 (not 7 as the question states). An equilateral triangle of side length 10 inches would have an area of 25*(root 3), which is approx. 43.3 inches2.
If the side length of an equilateral triangle is 5 centimeters what is the length of the altitude of the triangle?
Height = sqrt(3)/2 * length of side So here, approx 4.3301 cm
What is the height of an equilateral triangle with the side lengths of 8 inches?
To find the height of an equilateral triangle, you can use the formula: height = (√3/2) * side length. For an equilateral triangle with side lengths of 8 inches, the height would be (√3/2) * 8 inches, which simplifies to approximately 6.93 inches. This height represents the perpendicular distance from any vertex to the opposite side in an equilateral triangle.
