How to Calculate the Area of Trapezoids

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Area of Trapezoids

A trapezoid is a quadrilateral with one pair of parallel sides. Those parallel sides are the bases. The height is the perpendicular distance between the bases, not a slanted side.

Formula for the Area of a Trapezoid

The area formula is:

$A = \frac{1}{2}h(b_1 + b_2)$

In this formula, $b_1$ and $b_2$ are the base lengths and $h$ is the height. Add the bases first, multiply by the height, and take half. Area is written in square units.

Trapezoids

Formula Using the Midsegment

The trapezoid midsegment is the average of the bases:

$m = \frac{1}{2}(b_1 + b_2)$

Trapezoids2

Using the midsegment, the area is $A = mh$.

Example

If a trapezoid has bases of $8$ cm and $14$ cm and a height of $5$ cm, then $A = \frac{1}{2}(5)(8 + 14) = 55$. The area is $55$ square centimeters.

Area of Trapezoids

Think of this lesson as more than a rule to memorize. Area of Trapezoids is about shape relationships, formulas, and units. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.

Geometry formulas work because they measure a specific feature: length around, space inside, or space enclosed by a solid. Match the question to the measurement first.

Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.

Sketch or label the shape.
Decide whether the question asks for length, area, volume, or surface area.
Substitute values into the matching formula.
Keep units squared for area and cubed for volume.

A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.

Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.

When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.

On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.

Free printable Worksheets

Exercises for Area of Trapezoids

1) A trapezoid has bases $6$ cm and $10$ cm and height $4$ cm. Find its area.

2) A trapezoid has bases $9$ in and $15$ in and height $6$ in. Find its area.

3) A trapezoid has bases $7$ m and $13$ m and height $\frac{11}{2}$ m. Find its area.

4) A trapezoid has midsegment $11$ ft and height $8$ ft. Find its area.

5) A trapezoid has area $96$ square units and bases $10$ units and $14$ units. Find its height.

6) A trapezoid has area $117$, height $9$, and one base $12$. Find the other base.

7) A trapezoid has area $121$ square yd and bases $5$ yd and $17$ yd. Find its height.

8) A trapezoid has midsegment $15$ cm and height $13$ cm. Find its area.

9) A trapezoid has bases $18$ units and $24$ units and height $7$ units. Find its area.

10) A trapezoid has area $180$ square feet and height $12$ feet. What is its midsegment?

11) A trapezoid has bases $32$ m and $48$ m and height $20$ m. Find its area.

12) A trapezoid has horizontal bases $14$ and $8$ and height $6$. Find its area.

13) A trapezoid has area $90$. Every length is multiplied by $3$. What is the new area?

14) The bases are $x$ and $x + 6$, the height is $10$, and the area is $130$. Find the longer base.

15) The midsegment is $x + 4$, the height is $9$, and the area is $153$. Find $x$.

16) The bases differ by $8$ units and have average length $21$ units. Find the longer base.

17) A trapezoid has area $255$, height $15$, and one base $8$ units longer than the other. Find the longer base.

18) A trapezoid-shaped floor has area $260$ square feet. Flooring costs $\$4.50$ per square foot. Find the total cost.

19) Two trapezoids have areas from bases $10,16$ height $8$ and bases $16,20$ height $6$. Find the total area.

20) A trapezoid has bases $3x + 2$ and $5x - 4$, height $12$, and area $276$. Find the longer base.

Answers

1) Use $A = \frac{1}{2}h(b_1 + b_2)$.
Substitute: $A = \frac{1}{2}(4)(6 + 10)$.
Compute: $A = 32$.
Answer: $\color{red}{32\ \text{cm}^2}$

2) Use $A = \frac{1}{2}h(b_1 + b_2)$.
Substitute: $A = \frac{1}{2}(6)(9 + 15)$.
Compute: $A = 72$.
Answer: $\color{red}{72\ \text{in}^2}$

3) Use $A = \frac{1}{2}h(b_1 + b_2)$.
Substitute: $A = \frac{1}{2}(\frac{11}{2})(7 + 13)$.
Compute: $A = 55$.
Answer: $\color{red}{55\ \text{m}^2}$

4) Use the midsegment formula $A = mh$.
Substitute: $A = 11\cdot 8$.
Compute: $A = 88$.
Answer: $\color{red}{88\ \text{ft}^2}$

5) Set up $96 = \frac{1}{2}h(10 + 14)$.
Simplify the coefficient of $h$: $96 = 12h$.
Solve: $h = 8$.
Answer: $\color{red}{8\ \text{units}}$

6) Use $117 = \frac{1}{2}(9)(12 + b)$.
Divide by $\frac{9}{2}$: $26 = 12 + b$.
Solve: $b = 14$.
Answer: $\color{red}{14\ \text{units}}$

7) Set up $121 = \frac{1}{2}h(5 + 17)$.
Simplify the coefficient of $h$: $121 = 11h$.
Solve: $h = 11$.
Answer: $\color{red}{11\ \text{yd}}$

8) Use the midsegment formula $A = mh$.
Substitute: $A = 15\cdot 13$.
Compute: $A = 195$.
Answer: $\color{red}{195\ \text{cm}^2}$

9) Use $A = \frac{1}{2}h(b_1 + b_2)$.
Substitute: $A = \frac{1}{2}(7)(18 + 24)$.
Compute: $A = 147$.
Answer: $\color{red}{147\ \text{units}^2}$

10) Use $A = mh$.
Substitute: $180 = 12m$.
Solve: $m = 15$.
Answer: $\color{red}{15\ \text{ft}}$

11) Use $A = \frac{1}{2}h(b_1 + b_2)$.
Substitute: $A = \frac{1}{2}(20)(32 + 48)$.
Compute: $A = 800$.
Answer: $\color{red}{800\ \text{m}^2}$

12) Use the horizontal lengths as bases.
Substitute: $A = \frac{1}{2}(6)(14 + 8)$.
Compute: $A = 66$.
Answer: $\color{red}{66\ \text{square units}}$

13) Area scales by the square of the length factor.
The area factor is $3^2 = 9$.
New area: $90\cdot9 = 810$.
Answer: $\color{red}{810\ \text{square units}}$

14) Set up $130 = \frac{1}{2}(10)(2x + 6)$.
Simplify: $130 = 10x + 30$.
Solve: $x = 10$, so the longer base is $16$.
Answer: $\color{red}{16\ \text{units}}$

15) Use $A = mh$.
Substitute: $153 = 9(x + 4)$.
Solve: $x = 13$.
Answer: $\color{red}{13}$

16) The sum of the bases is $2\cdot21 = 42$.
Let the bases be $s$ and $s+8$.
Then $2s + 8 = 42$, so the longer base is $25$.
Answer: $\color{red}{25\ \text{units}}$

17) Set up $255 = \frac{1}{2}(15)(b + b + 8)$.
Divide by $7.5$: $34 = 2b + 8$.
The bases are $13$ and $21$.
Answer: $\color{red}{21\ \text{units}}$

18) Multiply area by price per square foot.
Compute $260\cdot4.50 = 1170$.
Use dollars for the final unit.
Answer: $\color{red}{\$1170}$

19) First area: $\frac{1}{2}(8)(10 + 16) = 104$.
Second area: $\frac{1}{2}(6)(16 + 20) = 108$.
Add: $104 + 108 = 212$.
Answer: $\color{red}{212\ \text{square units}}$

20) Set up $276 = \frac{1}{2}(12)(8x - 2)$.
Simplify: $276 = 48x - 12$, so $x = 6$.
The bases are $20$ and $26$.
Answer: $\color{red}{26\ \text{units}}$

How to Calculate the Area of Trapezoids