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 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
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.