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Quadrilateral Types of quadrilaterals Multiplication and division Area of a square Area of a rectangle Area of a triangleHere you will learn about the area of a quadrilateral, including how to find the area of a rectangle, square, parallelogram, and trapezoid.
Students will first learn about the area of a quadrilateral as part of measurement and data in third grade when they learn about the area of a rectangle.
They expand on this knowledge into 6th grade when they learn how to calculate the area of more complex shapes, such as parallelograms and trapezoids.
The area of a quadrilateral is the amount of space inside a quadrilateral.
To find the area of a quadrilateral, you can either count the number of unit squares within a shape or use the appropriate area formula for that shape.
Area is measured in square units. For example, square feet (ft^2), square inches (in^2), square meters (m^2), etc.
Area of a rectangle or area of a square = \text { base } \times \text { height }
For example,
This rectangle contains 15 squares.

Area of a parallelogram = \text { base } \times \text { height }
If we chop one end off of a parallelogram and rearrange it, 
A trapezoid is a quadrilateral with only one pair of parallel sides.
In order to find the area of a trapezoid, you need to decompose the shape into a rectangle and two triangles (or a rectangle and one triangle if it is a right trapezoid).
A quadrilateral is a closed 2 dimensional shape with 4 straight sides and 4 vertices.
Regular quadrilaterals have sides that are all the same length and interior angles that are the same size.
Irregular quadrilaterals have sides that have different lengths and interior angles that have different sizes.
There are several different types of quadrilaterals.
For example,
Square
A square is a closed 2 dimensional shape with four straight sides of equal length and four right angles (90 ^{\circ}) .
Rectangle
A rectangle is a closed 2 dimensional shape with four straight sides and four right angles (90^{\circ}) . It has two pairs of parallel sides that are equal.
Parallelogram
A parallelogram is a closed 2 dimensional shape with four straight sides. The opposite sides of a parallelogram have the same lengths and are parallel.
Rhombus
A rhombus is a parallelogram with four equal straight sides.
Trapezoid
A trapezoid, also known as a trapezium, is a closed 2 dimensional shape with four straight sides and only one pair of parallel sides.
How does this relate to 6th grade math?
In order to calculate the area of a rectangle, area of a square, or the area of a parallelogram:
In order to calculate the area of a trapezoid:
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEFind the area of the square:
Here the height is 8 . Since it is a square, the base is also 8 .
\begin{aligned}\text { Area } &=\text { base } \times \text { height } \\\\ \text { Area }&=8 \times 8\end{aligned}
2Complete the calculation.
\begin{aligned} & \text { Area }=8 \times 8 \\\\ & \text { Area }=64\end{aligned}
3Add the correct units.
The measurements on this square are in cm so the area will be measured in {cm}^2 .
\text { Area }=64 \mathrm{~cm}^2
Find the area of the rectangle:
Substitute the values into the formula. (Make sure the units are the same for all measurements.)
Here the base is 11 \, m and the height is 400 \, cm .
Notice that the base measurement is in meters and the height measurement is in centimeters.
The easiest thing to do here is to change 400 \, cm to 4 \, m so that both measurements are in meters.
(You could also change 11 \, m to 1,100 \,cm ).
\begin{aligned}\text { Area }&=\text { base } \times \text { height } \\\\ \text { Area }&=11 \times 4
\end{aligned}
Complete the calculation.
\begin{aligned} & \text { Area }=11 \times 4 \\\\ & \text { Area }=44\end{aligned}
Add the correct units.
The measurements on this rectangle are in m so the area will be in {m}^2 .
\text { Area }=44 \mathrm{~m}^2
Calculate the area of the parallelogram:
Substitute the values into the formula. (Make sure the units are the same for all measurements.)
\begin{aligned}\text { Area }&=\text { base } \times \text { height } \\\\ \text { Area }&=12 \times 8 \end{aligned}
Complete the calculation.
Area = 96
Add the correct units.
The measurements on this parallelogram are in mm so the area will be in {mm}^2 .
\text { Area }=96 \mathrm{~mm}^2
Calculate the area of the rhombus:
Substitute the values into the formula. (Make sure the units are the same for all measurements.)
\begin{aligned}\text { Area }&=\text { base } \times \text { height } \\\\ \text { Area }&=10 \times 12 \end{aligned}
Complete the calculation.
Area = 120
Add the correct units.
The measurements on this rhombus are in inches so the area will be {in}^2 .
\text { Area }=120 \mathrm{~in}^2
Find the area of the following trapezoid:
Decompose the shape into a rectangle and two triangles (or one triangle if it is a right trapezoid).
You can use the given measurements to label the base and height of the rectangle and each triangle.
You can also label each shape using the letters A, B , and C .
Find the area of each shape.
Shape A (triangle):
\begin{aligned}& \text { Area }=\cfrac{1}{2} \, b h \\\\ & \text { Area }=\cfrac{1}{2} \,(2 \times 5) \\\\ & \text { Area }=5\end{aligned}
Shape B (rectangle):
\begin{aligned}& \text { Area }=\text { base } x \text { height } \\\\ & \text { Area }=9 \times 5 \\\\ &\text { Area }=45\end{aligned}
Shape C (triangle):
\begin{aligned}& \text { Area }=\cfrac{1}{2} \, b h \\\\ & \text { Area }=\cfrac{1}{2} \, (2 \times 5) \\\\& \text { Area }=\cfrac{1}{2} \, \times 10 \\\\ & \text { Area }=5\end{aligned}
Add the areas together.
Add the area of the rectangle to the area of each triangle.
\begin{aligned}& \text { Area }=5+45+5 \\\\ & \text { Area }=55\end{aligned}
Add the correct units.
The measurements on this trapezoid are in cm , so the area will be in {cm}^2 .
\text { Area }=55 \mathrm{~cm}^2
Find the area of the following trapezoid:
Decompose the shape into a rectangle and two triangles (or one triangle if it is a right trapezoid).
Since this is a right trapezoid, it will need to be decomposed into a rectangle and one triangle. Label the two new shapes A and B .
Find the area of each shape.
Shape A (rectangle):
\begin{aligned}& \text { Area }=\text { base } x \text { height } \\\\ & \text { Area }=4 \times 5 \\\\ & \text { Area }=20\end{aligned}
Shape B (triangle):
\begin{aligned}& \text { Area }=\cfrac{1}{2} \, b h \\\\ & \text { Area }=\cfrac{1}{2} \,(4 \times 1) \\\\ & \text { Area }=\cfrac{1}{2} \times 4 \\\\ & \text { Area }=2\end{aligned}
Add the areas together.
\begin{aligned}& \text { Area }=20+2 \\\\ & \text { Area }=22\end{aligned}
Add the correct units.
The measurements on this trapezoid are in km so the area will be in {km}^2 .
\text { Area }=22 \mathrm{~km}^2
1. Quadrilateral ABCD , shown below, is a square. Find the area of the quadrilateral.
You can use the formula to find the area of the quadrilateral.
Since you know it is a square, you know all sides are the same length.
This means that since its height is 3{~m} , its base is also 3{~m} .
You can use these measurements and the area formula base \times height to calculate the area.
\begin{aligned}\text{Area }&=\text{ base }\times \text{ height}\\\\ &= 3 \times 3\\\\ &=9 \mathrm{~m}^{2}\end{aligned}
2. The base of the rectangle shown below is 4 times greater than its height. Find the area of the rectangle.
First, you need to find the height of the rectangle.
The problem states that the base of the rectangle is 4 times greater than its height.
This means you can divide the base measurement by 4 to get the height measurement.
28 \div 4=7
Once you know the height, you can use the formula for the area of a rectangle, which is base \times height .
\begin{aligned}\text { Area }& =\text { base } x \text { height } \\\\ & =28 \times 7 \\\\ & =196 \mathrm{~yd}^{2} \end{aligned}
3. Find the area of the parallelogram. Give your answer in square centimeters.
First, you need to make the units the same.
Since 1 {~cm} = 1 {~mm} , you can divide 70 {~mm} by 10 to get its value in cm.
70 {~mm} = 7 {~cm} .
Then you can use the area formula, base \times height .
\begin{aligned} \text{Area }&=\text{ base }\times \text{ height}\\\\ &= 7 \times 6\\\\ &=42 \mathrm{~cm}^{2} \end{aligned}
4. Find the area of the rhombus.
\begin{aligned} \text{Area }&=\text{ base }\times \text{ height}\\\\ &= 6 \times 8\\\\ &=48 \mathrm{~ft}^{2} \end{aligned}
5. Find the area of the trapezoid:
To find the area of the trapezoid, you must first decompose it into a rectangle and two triangles.
Use the area of a rectangle formula and the area of a triangle formula to find the area of each shape.
Then you can add the areas together to find the total area of the trapezoid.
A (triangle):
\begin{aligned} & \text { Area }=\cfrac{1}{2} \, b h \\\\ & \text { Area }=\cfrac{1}{2} \, (2 \times 6) \\\\ & \text { Area }=\cfrac{1}{2} \, \times 12 \\\\ & \text { Area }=6 \end{aligned}
B (triangle):
\begin{aligned} & \text { Area }=\text { base } \times \text { height } \\\\ & \text { Area }=5 \times 6 \\\\ & \text { Area }=30 \end{aligned}
C (triangle):
\begin{aligned} & \text { Area }=\cfrac{1}{2} \, b h \\\\ & \text { Area }=\cfrac{1}{2} \, (2 \times 6) \\\\ & \text { Area }=\cfrac{1}{2} \, \times 12 \\\\ & \text { Area }=6 \end{aligned}
\text { Total area }=6+30+6=42 \mathrm{~m}^2
6. Find the area of the right trapezoid:
First, you need to decompose the right trapezoid into a rectangle and a triangle.
Then, find the area of the rectangle and the area of the triangle using the formulas.
A (rectangle):
\begin{aligned} & \text { Area }=\text { base } \times \text { height } \\\\ & \text { Area }=16 \times 10 \\\\ & \text { Area }=160 \end{aligned}
B (rectangle):
\begin{aligned} & \text { Area }=\cfrac{1}{2} \, b h \\\\ & \text { Area }=\cfrac{1}{2} \, (2 \times 10) \\\\ & \text { Area }=\cfrac{1}{2} \, \times 20 \\\\ & \text { Area }=10 \end{aligned}
Add the area of the rectangle and the area of the triangle. Then add the correct units.
{Area} = 160 + 10
{Area} = 170 \mathrm{~ft}^{2}
A quadrilateral is a closed 2 dimensional shape with 4 straight sides and 4 vertices.
To find the area of a quadrilateral, such as a rectangle, square, or parallelogram, use the area formula which is base \times height .
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