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

**How to find the area of the shaded region?**

Step 1: Find area of inner shape

Step 2: Find area of outer shape

Step 3: Area of shaded region = area of outer shape – area of inner shape

#### How to Find the Area of a Rectangle Subtracted from Another Rectangle

#### Finding the Area of a Circle With Omitted Inscribed Triangle

#### Area and Circumference Examples

Some examples involving the area of triangles and circles. Also,
some examples to find the area of a shaded region.

Examples:

1) Find the area and perimeter of the following triangle.

2) Find the area and circumference of a circle with radius 8.

3) Find the area and circumference of a circle with diameter 10.

4) Find the area of the shaded region if the circle has diameter 6.

5) Find the area of the shaded region if the square has side 8.
This video explains how to determine an area formula for a
rectangular shaded region when the dimensions are given as variable
expressions.

Example: Determine a formula for the area of the orange shaded region.

Finding the area of a shaded region between an inscribed circle and a square.

Example: In the figure, a circle is inscribed in a square.

a. Find the area of the circle.

b. Find the area of the shaded region.
Finding the area of a shaded region between a square inscribed in a
circle.

Example: In the diagram, the square ABCD is inscribed in circle O with diagonal AC = 8. Find the number of square units in the area of the shaded region in terms of π.

This video shows how to find the area of a shaded region in a
circle. It uses area of sector and area of segment.
#### GMAT - Find the Area of the Shaded Region

Example: Viewed from the outside inward, the figure below depicts a square-circle-square-circle, each enclosed within the other. If the area of square ABCD is 2 square units, then which of the following expresses the area of the darkened corners of square EFGH?

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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, like the examples below.

Step 1: Find area of inner shape

Step 2: Find area of outer shape

Step 3: Area of shaded region = area of outer shape – area of inner shape

**Example:**

Find the area of the shaded region:

**Solution:**

Step 1: Find area of inner square = 2 cm × 2 cm = 4 cm^{2}

Step 2: Find area of outer shape = (2 cm × 3 cm) + (10 cm × 3 cm)

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

= 36 cm^{2}

Step 3: Area of shaded region = area of outer shape – area of inner square

= 36 cm^{2} – 4 cm^{2}

= 32 cm^{2}

Examples:

1) Find the area and perimeter of the following triangle.

2) Find the area and circumference of a circle with radius 8.

3) Find the area and circumference of a circle with diameter 10.

4) Find the area of the shaded region if the circle has diameter 6.

5) Find the area of the shaded region if the square has side 8.

Example: Determine a formula for the area of the orange shaded region.

Finding the area of a shaded region between an inscribed circle and a square.

Example: In the figure, a circle is inscribed in a square.

a. Find the area of the circle.

b. Find the area of the shaded region.

Example: In the diagram, the square ABCD is inscribed in circle O with diagonal AC = 8. Find the number of square units in the area of the shaded region in terms of π.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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