## Area of Quadrilaterals

When we’re asked to find the area of a quadrilateral, what we’re really looking for is the amount of space inside the boundaries or sides that connect to make the shape.

Let’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 × 5 field.

We can start with a strip of land that has $5$ blocks of grass.

$5$

$3$

And then we just need to copy this row $3$ times.

Now, we have $3$ rows of $5$ grass blocks, giving us a total of $3×5=15$ blocks.

This is area 😮. By multiplying the length by the width, we get the amount of space inside the sides of a rectangle.$A =l×w=3×5=15 $

Multiplying a shape's length (or base) by its width (or height) is a pattern you’ll notice when solving for the area of different quadrilaterals:

Shape | Image | Formula |

Rectangle | $A=l×w$ | |

Square | $A=l×w=s_{2}$ | |

Parallelogram | $A=b×h$ | |

Rhombus / Kite | $A=2p×q $ | |

Trapezoid | $A=2(b_{1}+b_{2})h $ |

Check out our calculator and lesson below to see how we find the area of trickier quadrilaterals.

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

### Area of Quadrilaterals Calculator

What does your quadrilateral look like?

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

$l=$

$w=$

$s=$

$b=$

$h=$

$p=$

$q=$

$b_{1}=$

$b_{2}=$

$h=$

#### Step 2. Multiply the length by the width.

$A =l×w=0×0=0 $So, our answer is $A=0$.### Recap 🧢 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.

$A=l×w$#### Step 1. Identify the side length of the square.

#### Step 2. Square the side length.

$A=s_{2}$Remember, all the sides of a square are equal to each other, so $l=w=s$.$A=l×w⟹A=s×s=s_{2}$#### Step 1. Identify the base and height of the parallelogram.

#### Step 2. Multiply the base by the height.

$A=b×h$Remember, a parallelogram can be rearranged to form a rectangle.$A=b×h⟹A=l×w$#### Step 1. Identify diagonal/cross lengths of the rhombus.

#### Step 2. Square the diagonal/cross lengths.

$A=2p×q $#### Step 3. Divide by $2$.

$A=2p×q $Remember, a rhombus can be rearranged to make a parallelogram.$A=2p×q ⟹A=2p ×q=b×h$#### Step 1. Identify the base lengths and height of the trapezoid.

#### Step 2. Add the base lengths.

$A=2(b_{1}+b_{2})h $#### Step 3. Multiply the sum of the base lengths by the height.

$A=2(b_{1}+b_{2})h $#### Step 4. Divide by $2$.

$A=2(b_{1}+b_{2})h $Remember, two trapezoids can be rearranged to make a parallelogram.$A=2(b_{1}+b_{2})h ⟹A=(b_{1}+b_{2})×h=b×h$

Continue to explore how to find the area of different types of quadrilaterals in more detail, starting with rectangles & squares.

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

### Rectangles & Squares

The formula for the area of a rectangle is $A=l×w$, where $l$ is the length of the rectangle and $w$ 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, $l=w=s$, we can also get the area of a square using $A=s_{2}$, where $s$ is the side of the square.

Let's start by finding the area of this rectangle:

$5$

$3$

$5$

$3$

Nice work! Remember, this is just like $3$ rows of $5$ blocks each, giving us $15$ total blocks:Now, let's try an example with a square ✨.

$3$

$5$

Find the area of this square:

$4$

$4$

Practice finding the area of rectangles and squares below 🔥 or keep scrolling to continue.Nice work! You're a master of rectangles and squares now. Next: parallelograms.

### Practice: Area of Rectangles & Squares

Question 1 of 4: Find the area of this quadrilateral ⬇️

$4$

$3$

$4$

$3$

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

$l=$

$w=$

#### Step 2. Multiply the length by the width

$A$$=$$l$$×$$w$$=$$×$

$=$

#### Step 4. Divide by 2.

$A$$=$

$224 $

$=$Nice work! Our answer is $A=12$.

### Parallelograms

The formula for the area of a parallelogram is $A=b×h$. Notice how it looks a lot like the formula for the area of a rectangle $A=l×w$.That’s because a parallelogram can be rearranged to form a rectangle:

$A=b×h⟹A=l×w$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.Let’s take a look at an example of how to solve for the area of a parallelogram.

Start by finding the area of this parallelogram:

$6$

$3$

$4$

$4$

$3$

$4$

$6$

$3$

$3$

Amazing job! Try one more, and find the area of this parallelogram:

$8$

$6$

$10$

$10$

$6$

$10$

$8$

$6$

$6$

Practice finding the area of parallelograms below 🔥🔥 or keep scrolling to continue.You got this! You're a master of parallelograms now. Next: rhombuses.

### Practice: Area of Parallelograms

Question 1 of 4: Find the area of this quadrilateral ⬇️

$12$

$2$

$4$

$4$

$2$

$4$

$12$

$2$

$2$

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

$b=$

$h=$

#### Step 2. Multiply the base by the height.

$A$$=$$b$$×$$h$$=$$×$

$=$

#### Step 4. Divide by 2.

$A$$=$

$248 $

$=$Nice work! Our answer is $A=24$.

### Rhombuses & Kites

The formula for the area of a parallelogram is $A=2p×q $.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 $2p $, and a height equal to $q$:

$A=2p×q =2p ×q⟹A=b×h$Let’s take a look at an example of how to solve for the area of a rhombus.

Start by finding the area of this rhombus:

$3$

$6$

$4$

$3$

$3$

$6$

$4$

Nice work! Now try another one:

$5$

$8$

$6$

$5$

$5$

$8$

$6$

Practice finding the area of rhombuses below 🔥🔥🔥 or keep scrolling to continue.You got this! You're a master of rhombuses too now. Lastly: trapezoids ✨.

### Practice: Area of Rhombuses

Question 1 of 4: Find the area of this quadrilateral ⬇️

$2$

$4$

$3$

$2$

$2$

$4$

$3$

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

$p=$

$q=$

#### Step 2. Multiply the diagonal/cross lengths.

$A$$=$$2p×q $$=$

$2$

$2$

$×$

$2$

$=$

$2$

#### Step 3. Divide by 2.

$A$$=$$212 $$=$

#### Step 4. Divide by 2.

$A$$=$

$212 $

$=$Nice work! Our answer is $A=6$.

### Trapezoids

The formula for the area of a trapezoid is $A=2(b_{1}+b_{2})h $.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 $b_{1}+b_{2}$, and a height equal to $h$:

$A=2(b_{1}+b_{2})h ⟹A=2×2(b_{1}+b_{2})h =b×h$Let’s take a look at an example of how to solve for the area of a trapezoid.

Let's start with this trapezoid:

$4$

$3$

$3$

$10$

$6$

$4$

$3$

$4$

$10$

$6$

$4$

Nice work! Let's find the area of one more trapezoid:

$3$

$5$

$5$

$8$

$4$

$3$

$5$

$3$

$8$

$4$

$3$

Practice finding the area of trapezoids on your own 🔥🔥🔥🔥 or keep scrolling to finish this lesson.

### Practice: Area of Trapezoids

Question 1 of 4: Find the area of this quadrilateral ⬇️

$2$

$4$

$4$

$10$

$8$

$2$

$4$

$2$

$10$

$8$

$2$

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

$b_{1}=$

$b_{2}=$

$h=$

#### Step 2. Add the base lengths together.

$A$$=$

$2$

$2(b_{1}+b_{2})×h $

$=$$($$+$$)×h$

$2$

$=$

$×h$

$2$

$2$

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

$A$$=$

$2$

$218×h $

$=$$18×$

$2$

$2$

$=$

$2$

#### Step 4. Divide by 2.

$A$$=$

$236 $

$=$Nice work! Our answer is $A=18$.

When you feel like you've mastered this lesson, click for a celebration ⬇️