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Area of Shaded Region



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

Area of Circle.

Example:

Calculate the shaded area:

area shaded region

Solution:
Area of inner square = 2 cm × 2 cm = 4 cm2

Area of outer shape = (2 cm × 3 cm) + (10 cm × 3 cm)
                                                        = 6 cm2 + 30 cm2
                                                        = 36 cm2

Shaded area = area of outer shape – area of inner square
                                = 36 cm2 – 4 cm2
                                = 32 cm2


 



Consecutive Odd Integers

Example 2: Consecutive Odd Integers

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

triangle

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 = 3x + 6

Isolate variable x

3x = 45 – 6

3x = 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

Consecutive Even Integers

Example 3: Consecutive Even Integers

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

4x + 12 = 60

Isolate variable x

4x = 60 – 12

4x = 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.


 



Videos

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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