These lessons help Grade 7 students learn how to find the area of shaded region involving polygons and circles.

**Related Pages**

Area Of Shaded Region Worksheet

Area Of Polygons

Area Of Circles

More Geometry Lessons

Grade 7 Math Lessons

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 2:**

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}

**Worksheets On Finding Areas Of Shaded Regions**
Involving Polygons

Circles And Polygons 1

Circles And Polygons 2

Circles And Polygons 3

Step 1: Find the area of the larger shape and the smaller shape.

Step 2: Subtract the areas.

Step 3: Write the units.

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

**Examples:**

- Find the area and perimeter of the following triangle.
- Find the area and circumference of a circle with radius 8.
- Find the area and circumference of a circle with diameter 10.
- Find the area of the shaded region if the circle has diameter 6.
- 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.

**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.

Use area of sector and area of segment.

**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?

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