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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

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

**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.

Frequently Asked Questions

Sheets of paper, tiles, diamonds, the tops of desks, books and erasers are some of the real-life examples of parallelograms.

Yes, a parallelogram is a special case of quadrilaterals with two pairs of opposite sides that are congruent as well as parallel.

This is not the case because a parallelogram is different from a rhombus, as a parallelogram has equal opposite sides, but in a rhombus we find that all the four sides are equal.

The base of any parallelogram is determined by dividing the area of the parallelogram by its height.