How To Find The Area Of A Trapezoidal Prism

Tabular array of Contents

1. What is a Trapezoid?
2. How to Observe the Area of a Trapezoid
3. Area of a Trapezoid Formula
• Using the Area of a Trapezoid Equation
4. Area of a Trapezoid Examples

What is a Trapezoid?

A trapezoid is a quadrilateral with one pair of parallel sides. Then, this iv-sided polygon is a plane figure and a closed shape. It has iv line segments and four interior angles. The parallel sides are the trapezoid'southward two bases; the other two sides are its legs.

Usually the trapezoid is presented with the longer parallel side -- the base -- horizontal. A perpendicular line from the base of operations to the other parallel side volition give you the trapezoid's acme or altitude.

What is an average in mathematics?

In mathematics, an boilerplate is the sum of a group of numbers divided past the quantity of items in the group.

So if y'all have three people holding books, y'all can find the average number of books they are holding like this: Martin is holding five books, Mack is holding 3 books, and Maria is belongings 4 books. Together, 12 books are existence held by three people. So, 12 books ÷ iii people = an average of 4 books each.

To find the area of a trapezoid, you lot volition detect the average length of the 2 bases.

How to Find the Area of a Trapezoid

To notice the expanse of any trapezoid, showtime past labeling its bases and altitude. In our trapezoid, label the longer base $a$ and the shorter base of operations $b$. Label a line perpendicular to the two bases $h$ for meridian or distance of the trapezoid.

Notice we did non label the legs. Nosotros do non need to know anything nearly the length of the legs or the angles of the vertices to detect expanse.

Area of a Trapezoid Formula

The formula for the expanse of a trapezoid is the average of the bases multiplied by the altitude. In the formula, the long and short bases are $a$ and $b$, and the distance is $h$:

Multiplying times $\frac{\mathrm{ane}}{\mathrm{ii}}$ is the same as dividing by 2. Nosotros take half the sum of the length of the ii bases (their average) and then multiply that by the altitude, or elevation, to discover the area in foursquare units.

Using the Area of a Trapezoid Equation

Trapezoid $\mathrm{50}\mathrm{1000}\mathrm{Due\; north}O$ has parallel bases $LM$ and $\mathrm{Due\; north}O$. Line segment $\mathrm{50}M$ is 7 cm long, and line segment $NO$ is 13 cm long. We will label longer side $NO$ every bit $a$ and shorter side $L\mathrm{Grand}$ as $b$. The height, $h$, is 5 cm.

First, let'southward plug these numbers into our formula:

$area=\frac{13c\mathrm{1000}+7c\mathrm{grand}}{2}\times 5c\mathrm{thousand}$

Next we add thirteen plus 7 and become:

$ar\mathrm{eastward}a=\frac{20c\mathrm{1000}}{2}\times 5cm$

Then nosotros dissever by two, then and get:

$ar\mathrm{due\; east}a=10ck\times \mathrm{v}cm$

Finally, nosotros multiply and go our answer:

$area=50c{m}^2$

The area of this trapezoid is 50 foursquare centimeters.

Area of a Trapezoid Examples

At present you effort it! Another trapezoid has a long base of operations $a$, 11 meters, and a shorter base $b$, 7 meters. Its altitude $h$ is 9 meters. What is the area in foursquare meters?

$area=\frac{\mathrm{eleven}cm+7cm}{2}\times 9cm$

Did y'all become 81 foursquare meters? Your respond for area is always in square units of the linear measurement. Then a trapezoid measured in feet gives an surface area in square anxiety, centimeters yield square centimeters, then on.

Call back that multiplying past ½ is the same as dividing by two, so y'all tin add together the lengths of the bases then divide their sum by ii, if that is easier for you.

Considering of the commutative property of multiplication, you can rearrange these iii numbers, $\frac{\mathrm{i}}{\mathrm{ii}}$, altitude $h$, and the length of bases $a+b$, in whatever society to brand the calculation easy.

So, with trapezoid $LMNO$, you lot could too have written the formula similar:

$area=\frac{1}{\mathrm{two}}\times \mathrm{nine}\times (11+7)$

Example #2

Here is ane more instance for yous. The new trapezoid is upside down from how y'all usually run into them, merely don't let that stop you! The short base $b$ is 21 inches long. The long base $a$ (this time at the top of the drawing) is 31 inches long. The altitude $h$ (no matter which fashion you look at the trapezoid) is five inches.

$area=\frac{\mathrm{ane}}{2}\times 5\times (31+21)$

OR

$ar\mathrm{east}a=\frac{\mathrm{ane}}{2}\times (31+21)\times 5$

OR

$area=\frac{31+21}{\mathrm{two}}\times 5$

Still you apply the formula, you volition always go the same respond: $area=130i{n}^2$

Lesson Summary

In this lesson and video we have reviewed what a trapezoid is, examined how averages have a function in geometry, learned how to label and utilize the parts of a trapezoid to calculate area, and learned the formula for calculating the area of a trapezoid in square units.

Next Lesson:

Heron's Formula

Source: https://tutors.com/math-tutors/geometry-help/how-to-find-the-area-of-a-trapezoid

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