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Multiplication and division Multiplying and dividing decimals Area of a rectangle Area of a parallelogram Area of a triangleHere you will learn about the area of composite shapes, including questions involving rectilinear shapes, composite shapes, missing side lengths and unit conversion.
Students will first learn about composite shapes as part of geometry in 3rd grade when they learn how to decompose and find the area of rectilinear shapes.
Students deepen their understanding of area in 4th grade, and extend their learning by finding the area of more complex shapes in 6th grade.
The area of composite shapes is the amount of space inside a shape composed of basic shapes put together. It is measured in square units (katex is not defined etc.).
Composite shapes can also be called compound shapes or composite figures.
To find the area of composite shapes, you must decompose the composite shape into basic shapes, then find the area of each of the basic shapes and add them together.
For example,
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katex is not defined |
Your final answer must be in square units. For example, square centimeters katex is not defined square meters katex is not defined square feet katex is not defined etc.
Use this worksheet to check your 3rd grade to 8th grade students’ understanding of calculating the area of composite shapes. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEUse this worksheet to check your 3rd grade to 8th grade students’ understanding of calculating the area of composite shapes. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEHow does this relate to 3rd grade math and 4th grade math?
Here’s how to find the area of composite shapes:
Find the area of the composite shape below:
Split the composite shape into two rectangles. You can do this in two ways:
For the purposes of this question you will use the first way.
2Find the measurements and area of the simpler shapes.
Label the two rectangles katex is not defined and katex is not defined
Area of Rectangle katex is not defined:
katex is not defined
Area of Rectangle katex is not defined:
katex is not defined
3Add the areas of the simpler shapes together.
katex is not defined
4Write down your final answer with square units.
katex is not defined
Find the area of the composite shape below:
Break down the composite shape into simpler shapes.
Split the composite shape into two rectangles and find the area of each rectangle.
Find the measurements and areas of the simpler shapes.
Label the two rectangles katex is not defined and katex is not defined
Area of Rectangle katex is not defined:
You need to calculate the unknown length. To do this, you need to use the measurements you are given in the question that are parallel to the unknown side:
If you add together the katex is not defined sides, you will get the length of rectangle katex is not defined
katex is not defined
katex is not defined
Area of Rectangle katex is not defined:
You need to calculate the unknown length. To do this, you need to use the measurements you are given in the question that are parallel to the unknown side:
The length of the entire composite shape is katex is not defined You need to subtract the katex is not defined of shape katex is not defined to get just the length of shape katex is not defined
katex is not defined
katex is not defined
Add the areas of the simpler shapes together.
katex is not defined
Write down your final answer with square units.
katex is not defined
The wall shown below needs to be painted. Each tin of paint covers a distance of katex is not defined square meters. How many tins of paint will be needed to cover the entire wall?
Break down the composite shape into simpler shapes.
Split the composite shape into three rectangles and find the area of each rectangle.
Find the measurements and areas of the simpler shapes.
Label the three rectangles katex is not defined and katex is not defined
Notice that rectangle katex is not defined and katex is not defined each have a tick mark at the bottom. This means that these sides are congruent, or equal. Therefore, we know the width of rectangle katex is not defined is katex is not defined
Area of Rectangle katex is not defined:
katex is not defined
Rectangle katex is not defined is congruent to Rectangle katex is not defined so you can just double the area of rectangle katex is not defined
katex is not defined
Area of Rectangle katex is not defined:
You need to calculate the unknown width. To do this, you need to use the measurements you are given in the question that are parallel to the unknown side:
The entire width of the shape is katex is not defined If you subtract katex is not defined and katex is not definedthe width of rectangles katex is not defined and katex is not defined
katex is not defined
katex is not defined
Add the areas of the simpler shapes together.
katex is not defined
Write down your final answer with square units.
katex is not defined
While this is the total area, you need to calculate how many tins of paint will be needed to cover the wall.
If each tin of paint covers a distance of katex is not defined square meters, you need to divide katex is not defined into katex is not defined
katex is not defined
Since you cannot buy katex is not defined of a can of paint, you need to round your answer to katex is not defined tins of paint.
Answer katex is not defined tins of paint will be needed.
Find the area of the composite shape below:
Break down the composite shape into simpler shapes.
Split the composite shape into a triangle and rectangle.
Note: This shape is a trapezoid. Another way to find the area of this shape would be to simply use the formula for the area of a trapezoid. For this question, because you are focusing on composite shapes, you will separate the shape into a triangle and a rectangle.
See also: Area of a trapezoid
Find the measurements and areas of the simpler shapes.
Label the two shapes katex is not defined and katex is not defined
Area of Triangle katex is not defined:
katex is not defined
Area of Rectangle katex is not defined:
You need to calculate the unknown length. To do this, you need to use the measurements you are given in the question that are parallel to the unknown side:
The height of the entire composite shape is katex is not defined You need to subtract the katex is not defined of shape katex is not defined to get just the length of shape katex is not defined
katex is not defined
katex is not defined
Add the areas of the simpler shapes together.
katex is not defined
Write down your final answer with square units.
katex is not defined
Calculate the value of katex is not defined in the composite shape below:
Break down the composite shape into simpler shapes.
Split the composite shape into two rectangles.
Find the measurements and area of the simpler shapes.
Label the two rectangles katex is not defined and katex is not defined
Area of Rectangle katex is not defined:
katex is not defined
In this case, you are not given enough information to find the area of Rectangle katex is not defined
Add the areas of the simpler shapes.
For this problem, you will need to use subtraction in order to find the area of rectangle katex is not defined
katex is not defined
Now that you know the area of rectangle katex is not defined you can calculate the value of katex is not defined
katex is not defined
katex is not defined
Below is a blueprint for a garden to be created in the middle of town. It will feature a triangular flowerbed and the remainder of the garden will be covered in grass.
Each roll of grass costs katex is not defined and covers a distance of katex is not defined square meters. How much will it cost to cover the garden with grass?
Break down the composite shape into simpler shapes.
Split the composite shape into two rectangles. Once you find the area of the two rectangles, you can subtract the area of the triangle.
Find the measurements and areas of the simpler shapes.
Label the three shapes katex is not defined and katex is not defined
Area of rectangle katex is not defined:
katex is not defined
Area of rectangle katex is not defined:
katex is not defined
Area of Triangle katex is not defined:
The height of the triangle is katex is not defined
You need to calculate the unknown width of the triangle. To do this, you need to use the measurements you are given in the question that are parallel to the unknown side:
The width of the entire composite shape is katex is not defined You need to subtract the katex is not defined and katex is not defined from katex is not defined to get the width of shape katex is not defined
katex is not defined
katex is not defined
Add the areas of the simpler shapes.
katex is not defined
Write down your final answer with square units.
katex is not defined
Use this worksheet to check your 3rd grade to 8th grade students’ understanding of calculating the area of composite shapes. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEUse this worksheet to check your 3rd grade to 8th grade students’ understanding of calculating the area of composite shapes. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREE1. Find the area of the composite shape below:
Split into two rectangles. Find the area of the rectangle and the area of the square and add them together.
Area of katex is not defined
Area of katex is not defined
Composite Area: katex is not defined
2. Find the area of the composite shape below:
Split into two rectangles. Find the area of the smaller rectangle and the larger rectangle and add them together.
Area of katex is not defined
Area of katex is not defined
Composite Area: katex is not defined
3. The wall shown below needs to be painted. Each tin of paint covers a distance of katex is not defined square meters. How many tins of paint will be needed to cover the entire wall?
Split into three rectangles:
Area of katex is not defined
Area of katex is not defined
Area of katex is not defined
Composite Area: katex is not defined
Then divide by katex is not defined to get the number of tins.
katex is not defined
Since you can’t buy katex is not defined of a tin, the answer will be rounded up to katex is not defined tins.
4. Find the area of the composite shape below:
Split into one rectangle and two triangles:
Since you know the triangles are congruent, you can use the base of the rectangle to find the base of the triangles.
katex is not defined
Area of katex is not defined
Area of katex is not defined
Area of katex is not defined
Composite Area: katex is not defined
5. Find the value of katex is not defined in the composite shape below:
Split into two rectangles:
Area of katex is not defined
The difference between the total area and the area of rectangle katex is not defined will give you the area of rectangle katex is not defined
katex is not defined
The area of rectangle katex is not defined divide by its width will give you the missing side length:
katex is not defined
The difference between the length of rectangle katex is not defined and the length of rectangle katex is not defined gives you the value of missing side length katex is not defined
katex is not defined
6. An architect is developing a blueprint for one floor of a house which is shown below. The shaded region represents the floor and will need to be fully tiled. Each square tile has a width of katex is not defined How many tiles will be needed to cover the entire floor?
To find the area of the shaded region, you need to first find the total area of the rectangle. Then find the area of the triangle.
Instead of adding the areas together, here you will be subtracting the areas.
Area of katex is not defined
Area of katex is not defined
katex is not defined
Area of katex is not defined tile katex is not defined
katex is not defined tiles
katex is not defined tiles
A composite is a shape composed of basic shapes put together. A composite shape can also be called a compound shape or a composite figure.
To find the area of composite shapes, you must decompose the composite shape into basic shapes, then find the area of each of the basic shapes and add them together.
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