 Videos, worksheets, examples, and solutions 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, like the examples below.

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

Example:

Find the area of the shaded region: Solution:
Step 1: Find area of inner square = 2 cm × 2 cm = 4 cm2

Step 2: Find area of outer shape = (2 cm × 3 cm) + (10 cm × 3 cm)
= 6 cm2 + 30 cm2
= 36 cm2

Step 3: Area of shaded region = area of outer shape – area of inner square
= 36 cm2 – 4 cm2
= 32 cm2

Worksheets on Finding Areas of Shaded Regions
Involving Polygons
Circles & Polygons 1
Circles & Polygons 2
Circles & Polygons 2

#### How to find the area of shaded region of a rectangle within another rectangle?

Step 1: Find the area of the larger shape and the smaller shape.
Step 2: Subtract the areas.
Step 3: Write the units.

#### 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. 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. How to find 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. How to find 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.

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?

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