## Slant Height Formula

The distance is calculated across a lateral face from the base to the apex at the “centre” of the face is the slant height of such an item (including a frustum, or pyramid). In other terms, it’s the height of the lateral face of a triangle.

The slant height is the distance around the outside of the cone from the tip to the bottom.

To determine the overall slant height of a pyramid or a cone, possibly look within the picture. As an instance, let’s cut apart a cone. To get two halves, we first dramatically cut through the conical from vertex position A to segment BC. Either half’s sliced surface is in the configuration of an isosceles, which would be a triangle having two equal-length sides. The cone’s slant height was determined by those two sides. We now have a triangle ABC with the same length sides AB and AC.

Now, we’ll draw the cone’s altitude from A right down to BC, making a right angle. Pointer M is the intersection of altitude and BC. The triangular AMC is a right angle in which AM is the elevation and AC is the original cone’s slant height. Since it is the face opposing the right angle, AC is the hypotonia use of the right triangle.

If we chopped up the figure as we have done in this example, each cone and pyramid include a right triangle. The Pythagorean theorem, a2 + b2 = c2, can be used to compute the slant height. The height of the altitude will be both for cones and pyramids, and the slant height will be c. The radius of a circle that serves as the base of a cone is b. The ratio of the distance between the base’s center and one of its edges. b represents half the size of the side of the picture that serves as the base of a pyramid.

## Solved Example

We know that the Pythagorean Formula a2 + b2 = c2 could be used, where an is the height, b is half the base length, and c seems to be the slant height. Substituting a = 12 & b = (1/2)(10) = 5 into our data, we get

c2 = 122 + 52

c2 = 144 + 25

c2 = 169

c = 13

The slant is 13 feet tall.