Area of Trapezoids Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Area of Trapezoids.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The area of a trapezoid is half the sum of its two parallel bases multiplied by the height: $A = \frac{1}{2}(b_1 + b_2)h$ .

Two identical trapezoids fit together to form a parallelogram. The trapezoid is half of that parallelogram.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A trapezoid's area is the average of its two parallel bases multiplied by the perpendicular height between them.

Common stuck point: The procedure for area of trapezoids is the easy part; the trap is multiplying only one base by the height. Asking "Do I have two parallel bases of different lengths and the perpendicular height between them?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Do I have two parallel bases of different lengths and the perpendicular height between them?

Worked Examples

Example 1

medium

A trapezoidal deck has bases

12

ft and

20

ft and height

9

ft. Find its area.

Trapezoidal deck: bases 12 ft and 20 ft, height 9 ft — find the area

Answer

144 ft²

First step

A=\tfrac{1}{2}(12+20)(9)=\tfrac{1}{2}(32)(9)

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Example 2

medium

A trapezoid has vertices

(0,0)

(10,0)

(7,5)

(2,5)

. Find its area.

Example 3

medium

An isosceles trapezoid has parallel sides

6

and

14

and legs of

5

. Find its area.

Isosceles trapezoid: bases 6 and 14, legs 5 — find the area

Example 4

hard

A right trapezoid has bases

8

and

12

and one leg perpendicular to the bases measuring

5

. Find its area.

Example 5

hard

A trapezoid is split by its midsegment into two smaller trapezoids of equal height. If bases are

6

and

14

and total height is

8

, find the area of the upper smaller trapezoid (bases

6

and midsegment).

Upper trapezoid after midsegment split: bases 6 and 10, height 4 — find the area

Example 6

hard

An isosceles trapezoid has parallel sides

4

and

10

and height

4

. Find each leg.

Isosceles trapezoid: bases 4 and 10, height 4 — find each leg

Example 7

hard

A trapezoid is split into a rectangle and two triangles. Bases are

8

(top) and

14

(bottom), height

6

, and the trapezoid is isosceles. Show the rectangle has area

48

Isosceles trapezoid: bases 8 and 14, height 6 — show the embedded rectangle has area 48

Example 8

hard

A trapezoidal swimming pool is

20

m and

30

m on its parallel sides,

12

m perpendicular distance between them, and

2

m deep throughout. Find the volume.

Pool cross-section: parallel sides 20 m and 30 m, perpendicular distance 12 m — find the cross-section area, then volume for depth 2 m

Example 9

challenge

A trapezoid has diagonals

10

and

24

that meet at right angles. Find its area.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Find the area of a trapezoid with parallel sides

4

and

8

and height

5

Find the area: bases 4 and 8, height 5

Example 2

easy

Find the area of a trapezoid with bases

3

and

7

and height

4

Find the area: bases 3 and 7, height 4

Example 3

easy

What part of a trapezoid is the height?

Example 4

easy

A trapezoid has bases

4

and

4

and height

6

. What shape and what area?

Example 5

easy

In a trapezoid, which two sides are called bases?

Example 6

medium

A trapezoid has area

100

, height

10

, and one base

6

. Find the other base.

Area = 100, b₁=6, height 10 — find b₂

Example 7

medium

A trapezoid's midsegment is

9

and height is

7

. Find its area.

Example 8

medium

A trapezoid has parallel sides

9

and

15

and area

96

. Find the height.

Area = 96; bases 9 and 15 — find the height

Example 9

medium

A trapezoidal sign has bases

30

in and

50

in and height

24

in. Find its area in square feet.

Example 10

medium

A trapezoid's area triples when its height triples (bases unchanged). True or false, and why?

Example 11

hard

A trapezoidal cross-section has bases

4

m (bottom) and

10

m (top) and depth

3

m. Find the area.

Example 12

hard

A trapezoid has bases in ratio

1:3

and height

8

, with area

80

. Find both bases.

Bases in ratio 1:3, height 8, area 80 — verify bases 5 and 15

Example 13

hard

A trapezoid has area

120

with bases

b_1=10

b_2=14

. Find the height.

Area = 120; bases 10 and 14 — find the height

Example 14

hard

Two trapezoids share the same height and same average base length. How do their areas compare?

Example 15

challenge

Why does the trapezoid formula

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

reduce to the rectangle formula when

b_1=b_2=b

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Related Concepts

Area of Parallelograms Area of Triangles

Background Knowledge

These ideas may be useful before you work through the harder examples.

area of parallelogramsarea of triangles