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Videos, worksheets, stories and songs to help Grade 7 students learn how to find the area of
shaded region involving polygons and circles.

Sometimes, you may be required to calculate the area of shaded
regions. Usually, we would subtract the area of a smaller inner
shape from the area of a larger outer shape in order to find the
area of the shaded region. If any of the shapes is a composite shape
then we would need to subdivide it into shapes that we have area
formulas, for example

Area of Polygons: triangle, square, rectangle, parallelogram, rhombus, kite, trapezoid, regular polygon

**Example:**

Calculate the shaded area:

**Solution:**

Area of inner square = 2 cm × 2 cm = 4 cm^{2}

Area of outer shape = (2 cm × 3 cm) + (10 cm × 3 cm)

= 6 cm^{2} + 30 cm^{2}

= 36 cm^{2}

Shaded area = area of outer shape – area of inner square

= 36 cm^{2} – 4 cm^{2}

= 32 cm^{2}

The lengths of the sides of a triangle are consecutive odd numbers. What is the length of the longest side if the perimeter is 45?

Solution:

Step 1: Being consecutive odd numbers we need to add 2 to the previous number.

Assign variables :

Let

x= length of shortest side

x+ 2 = length of medium side

x+ 4 = length of longest side

Sketch the figure

Step 2: Write out the formula for perimeter of triangle.

P=sum of the three sides

Step 3: Plug in the values from the question and from the sketch.

45 =

x + x +2 +x+ 4

Combine like terms

45 = 3

x+ 6

Isolate variable *x*

3

x= 45 – 63

x= 39

x=13

Step 3: Check your answer

13 + 13 + 2 + 13 + 4 = 45

Be careful! The question requires the length of the longest side.

The length of longest = 13 + 4 =17

Answer: The length of longest side is 17

John has a board that is 5 feet long. He plans to use it to make 4 shelves whose lengths are to be a series of consecutive even numbers. How long should each shelf be in inches?

Solution:

Step 1: Being consecutive even numbers we need to add 2 to the previous number.

Assign variables :

Let

x= length of first shelf

x+ 2 = length of second shelf

x+ 4 = length of third shelf

x+ 6 = length of fourth shelf

Step 2: Convert 5 feet to inches

5 × 12 = 60

Step 3: Sum of the 4 shelves is 60

x + x +2 +x+ 4 +x+ 6 = 60

Combine like terms

4

x+ 12 = 60

Isolate variable *x*

4

x= 60 – 124

x= 48

x= 12

Step 3: Check your answer

12

+12+2 + 12 + 4 + 12 + 6 = 60

The lengths of the shelves should be 12, 14, 16 and 18.

Answer: The lengths of the shelves in inches should be 12, 14, 16 and 18.

This video shows how to find consecutive integers, consecutive odd integers, & consecutive even integers that add up to a given number.

The following video shows how to solve the integer word problems:

The sum of two consecutive integers is 99. Find the value of the smaller integer.

The sum of two consecutive odd integers is 40. What are the integers?

The sum of three consecutive even integers is 30. Find the integers.

The following video gives another example of how to solve consecutive integer word problems.

The sum of three consecutive integers is 24. Find the integers.

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