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Split the following shapes into rectangles and find their areas. (The measures are given in centimetres).

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Detailed Solution

Here, the given figures can be further divided into rectangles,

We know that, Area of the rectangle = length × breadth

and the Area of the square = length × length

(a) Here, the area of the rectangle I = 10 cm × 2 cm = 20 sq. cm

Here, the area of the rectangle II = 10 cm × 2 cm = 20 sq. cm

The total area of the figure is therefore equal to the sum of the area of the two rectangles.

= 20 sq. cm + 20 sq. cm = 40 sq. cm.

(b) Here, the area of the square I = 7 cm × 7 cm = 49 sq. cm

Here, the area of the square II = 7 cm × 7 cm = 49 sq. cm

Here, the area of the square III = 7 cm × 7 cm = 49 sq. cm

Here, the area of the square IV = 7 cm × 7 cm = 49 sq. cm

Here, the area of the square V = 7 cm × 7 cm = 49 sq. cm

The total area of the figure is therefore equal to the sum of the area of the rectangles and two squares.

= 49 sq. cm + 49 sq. cm + 49 sq. cm + 49 sq. cm + 49 sq. cm = 245 sq. cm.

Here, the area of the rectangle II = 4 cm × 1 cm = 4 sq. cm

The total area of the figure is therefore equal to the sum of the area of the two rectangles.

= 5 sq. cm + 4 sq. cm = 9 sq. cm.

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