# How to find the height, if you know the length and width

At the base of many geometric shapes are rectangles and squares. The most common among them a box. This also includes a cube, a pyramid and a truncated pyramid. All four of these shapes have a parameter called height.

## Instruction how to find the height, if you know the length and width

Step 1:

Draw a simple isometric shape, called a rectangular parallelepiped. It got its name for the reason that its faces are rectangles. The base is also of rectangular parallelepiped having a length and a width b.

Step 2:

The volume of a cuboid is equal to the product of the area of the base to a height of: V = S * h. Since the base is a rectangle parallelepiped, this base area is S = a * b, where a - length, b - width. Hence, the volume is V = a * b * h, where h - height (wherein, h = c, where c - parallelepiped edge). If the problem is to find the height of the box, convert the last formula as follows: h = V / a * b.

Step 3:

There are rectangular parallelepipeds, in the grounds of which are squares. All its faces are rectangles, of which two squares are. This means that its volume is equal to V = h * a ^ 2, where h - height of the parallelepiped, a - square length equal width. Accordingly, the height of the figure found as follows: h = V / a ^ 2.

Step 4:

The cube squares with the same parameters are all six faces. The formula for calculating the scope is as follows: V = a ^ 3. Calculate any of the parties, if we know the other is not required, since all of them are equal.

Step 5:

All of these methods require the calculation of height through the volume of the box. However, there is another way to calculate the height of a given width and length. It is used in the case in the problem instead of the volume shows the area. The area of the box is equal to S = 2 * a ^ * b ^ 2 2 * c ^ 2. Hence, c (height parallelepiped) is a = sqrt (s / (2 * a ^ 2 * b ^ 2)).

Step 6:

There and other objects of calculating the height for a given length and width. Some of them appear pyramid. If the problem is given the angle at the base plane of the pyramid, as well as its length and width, get high, using the Pythagorean theorem and properties of angles.

Step 7:

To find the height of the pyramid, first determine the diagonal base. From the figure it can be concluded that the diagonal is d = √a ^ 2 + b ^ 2. Since the height of fall in the center of the base, half diagonally find follows: d / 2 = √a ^ 2 + b ^ 2/2. The height of the find, using the properties of tangent: tgα = h / √a ^ 2 + b ^ 2/2. It follows that the height is h = √a ^ 2 + b ^ 2/2 * tgα.