You can find the area of a trapezoid by using the formula

\(\displaystyle \text{Area} = h\cdot \frac{b_1+b_2}{2} \)

where \(b_1\) and \(b_2\) are the two parallel sides (or “bases”) and \(h\) is the height of the trapezoid.

 

Notes

 

Practice Problems

Find the area of the following trapezoids.

\(\textbf{1)}\)

Show Answer

The answer is \( 400 \) cm\(^2 \)

Show Work

\(\,\,\,\,\,\,\text{Area}=\displaystyle h \cdot \left(\frac{b_1+b_2}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 10 \cdot \left(\frac{35+45}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 10 \cdot \left(\frac{80}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 10 \cdot \left(40\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 400\)
\(\,\,\,\,\,\,\)The answer is \( 400 \) cm\(^2 \)

 

\(\textbf{2)}\)

Show Answer

The answer is \( 280 \) in\(^2 \)

Show Work

\(\,\,\,\,\,\,\text{Area}=\displaystyle h \cdot \left(\frac{b_1+b_2}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 8 \cdot \left(\frac{30+40}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 8 \cdot \left(\frac{70}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 8 \cdot \left(35\right)\)
\(\,\,\,\,\,\,\)The answer is \( 280 \) in\(^2 \)

 

\(\textbf{3)}\)

Show Answer

The answer is \( 27 \) ft\(^2 \)

Show Work

\(\,\,\,\,\,\,\text{Area}=\displaystyle h \cdot \left(\frac{b_1+b_2}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 3 \cdot \left(\frac{7+11}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 3 \cdot \left(\frac{18}{2}\right)\)
\(\,\,\,\,\,\,\text{Area}=\displaystyle 3 \cdot \left(9\right)\)
The answer is \( 27 \) ft\(^2 \)

 

\(\textbf{4)}\) Find the area of the trapezoid with the following vertices. \((0,0), (2,8), (6,8), (8,0)\)

Show Answer

The answer is \( 48 \) units\(^2 \)

 

\(\textbf{5)}\) Find the area of the following trapezoid.

Show Answer

The answer is \( 84 \) units\(^2 \)

 

Challenge Problems

\(\textbf{6)}\) Solve for x if the area = \( 200 \) units\(^2 \).

Show Answer

The answer is \( x=8 \)

 

\(\textbf{7)}\) Solve for y if the area = \( 196 \) units\(^2 \).

Show Answer

The answer is \( y=14 \)

 

\(\textbf{8)}\) Solve for x if the area = \( 90 \) units\(^2 \).

Show Answer

The answer is \( x=6 \)

 

See Related Pages\(\)

\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Trapezoid Area Calculator (Omnicalculator.com)}\)
\(\,\,\,\,\,\,\,\,\)\(\)

\(\bullet\text{ Area and Perimeter of Rectangles}\)
\(\,\,\,\,\,\,\,\,\)\(\,\, A=bh, \,\, P=2b+2h…\)

\(\bullet\text{ Area and Perimeter of Triangles}\)
\(\,\,\,\,\,\,\,\,\)\(\,\, A=\frac{1}{2}bh, \,\, P=s_1+s_2+s_3…\)

\(\bullet\text{ Area and Circumference of Circles}\)
\(\,\,\,\,\,\,\,\,\)\(\,\, A= \pi r^2, \,\,C=2 \pi r…\)

\(\bullet\text{ Area of Trapezoids}\)
\(\,\,\,\,\,\,\,\,\)\(A=\frac{1}{2}(b_1+b_2)\cdot h…\)

\(\bullet\text{ Area of Compound Figures}\)
\(\,\,\,\,\,\,\,\,\)\(\)

\(\bullet\text{ Andymath Homepage}\)

 

In Summary

A trapezoid is a quadrilateral containing a pair of parallel sides, called the bases, and two non-parallel sides, called the legs. They are often referred to as a “trapezium” outside of the United States. The area of a trapezoid is typically covered in a high school geometry class. It is often introduced along with other two-dimensional shapes, such as triangles and circles, and students learn how to calculate the area of each using specific formulas. The formulas can also be used to find particular parts of the trapezoids given the area. Isosceles trapezoids are a special case where the legs and base angles are congruent.