Height of a Parallelogram Formulas | List of Height of a Parallelogram Formulas You Should Know - BYJUS

# Height of a Parallelogram Formulas

The height of a parallelogram is defined as the shortest distance between the opposite sides of this quadrilateral. In the following article, the formula will be introduced as well as looking at a few examples that focus on finding the height of a parallelogram by applying the relevant formula....Read MoreRead Less

### What is the Formula to Find the Height of a Parallelogram?

The height of a parallelogram, also known as the altitude of a parallelogram, is defined as the perpendicular distance between any of its two parallel sides. The formula to find the height of a parallelogram is as follows.

$$h=\frac{A}{b}$$

In this formula,

h = height of the parallelogram

b = base of the parallelogram

A = Area of the parallelogram

### Solved Examples

Example 1: If the base of a parallelogram is $$30$$ inches long and its area is $$180$$ square inches, determine the height of this parallelogram.

Solution:

The details provided in the question,

Area of the parallelogram, $$A=180$$ in$$^2$$

Base, $$b=30$$ in

The formula to find the height of a parallelogram is,

$$h=\frac{A}{b}$$            Write the formula

$$h=\frac{180}{30}$$          Substitute the values

$$h=6$$              Divide

Hence, the height of the parallelogram is $$6$$ inches.

Example 2: What is the total area of nine solar panels each in the shape of a parallelogram, with a base length of $$4$$ feet and corresponding altitude measure $$3$$ feet?

Solution:

$$A=b\times h$$           Write the formula for area

$$A=4\times 3$$           Substitute $$4$$ for $$b$$ and $$3$$ for $$h$$

$$A=12$$ ft$$^2$$           Multiply

Area of nine solar panels $$=9~\times$$ area of a solar panel

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=9\times 12$$

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=108$$ ft$$^2$$

So, the area of nine solar panels is $$108$$ square feet.

Example 3: A parallelogram-shaped ceramic tile has a $$10$$ inch base and is $$4$$ inches in height. Find the area of the tile.

Solution:

It is mentioned that the base of the tile is $$10$$ inches long and the height is $$4$$ inches long.

By using the formula for the height of a parallelogram, we can determine the area of the tile.

So,

$$h=\frac{A}{b}$$

$$h\times b=A$$

$$4\times 10=A$$

$$40=A$$

Therefore, the area of the tile is $$40$$ square inches.