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Introduction

QUICK LINKS


Introduction

Area of Quadrilaterals

INTRO
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When weโ€™re asked to find the area of a quadrilateral, what weโ€™re really looking for is the amount of space inside the boundaries or sides that connect to make the shape.
Letโ€™s imagine we want to build a small field in a Minecraft world and need to figure out the amount of land (area) in a 3 ร— 5 field.
We can start with a strip of land that has blocks of grass.
And then we just need to copy this row times.
Now, we have rows of grass blocks, giving us a total of blocks.
This is area ๐Ÿ˜ฎ. By multiplying the length by the width, we get the amount of space inside the sides of a rectangle.
Multiplying a shape's length (or base) by its width (or height) is a pattern youโ€™ll notice when solving for the area of different quadrilaterals:
ShapeImageFormula
Rectangle
Square
Parallelogram
Rhombus / Kite
Trapezoid
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to find the area of quadrilaterals and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

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CALCULATOR
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Area of Quadrilaterals Calculator

What does your quadrilateral look like?

Step 1. Identify the length & width of the rectangle.

Step 2. Multiply the length by the width.

So, our answer is .
KEY STEPS
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How to Find the Area of a Quadrilateral

Shape:

Step 1. Identify the length & width of the rectangle.

Step 2. Multiply the length by the width.

Step 1. Identify the side length of the square.

Step 2. Square the side length.

Remember, all the sides of a square are equal to each other, so .

Step 1. Identify the base and height of the parallelogram.

Step 2. Multiply the base by the height.

Remember, a parallelogram can be rearranged to form a rectangle.

Step 1. Identify diagonal/cross lengths of the rhombus.

Step 2. Square the diagonal/cross lengths.

Step 3. Divide by .

Remember, a rhombus can be rearranged to make a parallelogram.

Step 1. Identify the base lengths and height of the trapezoid.

Step 2. Add the base lengths.

Step 3. Multiply the sum of the base lengths by the height.

Step 4. Divide by .

Remember, two trapezoids can be rearranged to make a parallelogram.
LESSON
โ€” Area of Rectangles & Squares

Area of Rectangles & Squares

The formula for the area of a rectangle is , where is the length of the rectangle and is the width.

We can use the same formula for finding the area of a square.
Since all the side lengths are equal in a square, , we can also get the area of a square using , where is the side of the square.

EXAMPLE 1

Let's start by finding the area of this rectangle:
Nice work! Remember, this is just like rows of blocks each, giving us total blocks:
Now, let's try an example with a square โœจ.

EXAMPLE 2

Find the area of this square:
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're dealing with parallelograms.
PRACTICE
โ€” Area of Rectangles & Squares

Practice: Area of Rectangles & Squares

Question 1 of 4: Find the area of this quadrilateral โฌ‡๏ธ

Step 1. Identify the length & width of the rectangle.

Step 2. Multiply the length by the width

Step 4. Divide by 2.

Nice work! Our answer is .
LESSON
โ€” Area of Parallelograms

Area of Parallelograms

The formula for the area of a parallelogram is . Notice how it looks a lot like the formula for the area of a rectangle .

Thatโ€™s because a parallelogram can be rearranged to form a rectangle:
The base of a parallelogram corresponds to the length of a rectangle, and the height of a parallelogram corresponds to the width of a rectangle.
Letโ€™s take a look at an example of how to solve for the area of a parallelogram.

EXAMPLE 1

Start by finding the area of this parallelogram:

EXAMPLE 2

Amazing job! Try one more, and find the area of this parallelogram:
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're dealing with rhombuses.
PRACTICE
โ€” Area of Parallelograms

Practice: Area of Parallelograms

Question 1 of 4: Find the area of this quadrilateral โฌ‡๏ธ

Step 1. Identify the base & height of the parallelogram.

Step 2. Multiply the base by the height.

Step 4. Divide by 2.

Nice work! Our answer is .
LESSON
โ€” Area of Rhombuses & Kites

Area of Rhombuses & Kites

The formula for the area of a parallelogram is .

It may not be obvious at first, but if we split a kite or rhombus into two identical pieces, we can rearrange them to form a parallelogram with a base equal to , and a height equal to :
Letโ€™s take a look at an example of how to solve for the area of a rhombus.

EXAMPLE 1

Start by finding the area of this rhombus:

EXAMPLE 2

Nice work! Now try another one:
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're dealing with trapezoids.
PRACTICE
โ€” Area of Rhombuses & Kites

Practice: Area of Rhombuses & Kites

Question 1 of 4: Find the area of this quadrilateral โฌ‡๏ธ

Step 1. Identify the diagonal/cross lengths of the rhombus.

Step 2. Multiply the diagonal/cross lengths.



Step 3. Divide by 2.

Step 4. Divide by 2.

Nice work! Our answer is .
LESSON
โ€” Area of Trapezoids

Area of Trapezoids

The formula for the area of a trapezoid is .

It may not be obvious at first, but if we have two identical trapezoids, we can rearrange them to form a parallelogram with a base equal to , and a height equal to :
Letโ€™s take a look at an example of how to solve for the area of a trapezoid.

EXAMPLE 1

Let's start with this trapezoid:

EXAMPLE 2

Nice work! Let's find the area of one more trapezoid:
Awesome! If youโ€™d like to practice additional problems with trapezoids, expand the
Practice
below before closing out this lesson! โšก
PRACTICE
โ€” Area of Trapezoids

Practice: Area of Trapezoids

Question 1 of 4: Find the area of this quadrilateral โฌ‡๏ธ

Step 1. Identify the base lengths and height of the trapezoid.

Step 2. Add the base lengths together.



Step 3. Multiply the sum of the base lengths by the height.



Step 4. Divide by 2.

Nice work! Our answer is .
CONCLUSION
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Incredible work, look at you go! Thanks for checking out this lesson โ˜บ๏ธ๐Ÿ™. Where to next?
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