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Finding The Area Of The Shaded Region Step-By-Step (2 Different Ways)

There are two ways to solve this:

1st Way

The first way is to divide this into two parts.

Firstly find the area of a smaller rectangle and then the area of the total rectangle.

Then subtract the area of the smaller triangle from the total area of the rectangle.

1st way is to split the whole rectangle into 2 parts

Area of the smaller rectangle

Width of white rectangle = 30cm – 8cm = 22cm
Length of white rectangle = 15cm – 4cm = 11cm
Area of white rectangle = 22cm * 11cm = 242 cm^2

The total area of the rectangle

Area of total rectangle = 30cm * 15cm = 450cm^2

Area of the shaded region

Area of shaded area = 450cm – 242cm = 208cm^2

2nd Way

The second way is to divide the shaded part into 3 rectangles.

Then add the area of the all 3 rectangles to get the area of the shaded region.

Split the shaded region into 3 parts

Rectangle A

Area of rectangle A = 8cm * 11cm = 88cm^2

Rectangle B

Area of rectangle B = 8cm * 4cm = 32cm^2

Rectangle C

Area of rectangle C = 22cm * 4cm = 88cm^2

Area of the shaded region

Area of shaded area = 88cm^2 + 32cm^2 +88cm^2 = 208cm^2

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