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
Rapid Recall
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.
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.