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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.

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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.


Calculate the shaded area:

area shaded region

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


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.

This video explains how to determine an area formula for a rectangular shaded region when the dimensions are given as variable expressions.


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

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

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


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