A picture is pasted in the centre of a board which is 20 cm long and 16 cm broad. If this leaves a vacant strip of breadth 3.5 cm around the picture, find the area of the strip.

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Solution

Let PQRS be the board that has a strip along it, measuring 3.5 cm. From the information, we get the figure ABCD that is also a rectangle.
Length of PQRS = 20 cm
Breadth of PQRS = 16 cm
Area of PQRS = length × breadth
= 20 × 16 cm²
= 320 cm²
Now, there is a strip measuring 3.5 cm.
∴ Length of ABCD = 20 – 3.5 – 3.5 cm = 13 cm
Breadth of ABCD = 16 – 3.5 – 3.5 = 9 cm
Area of ABCD = length × breadth
= 13 × 9 cm²
= 117 cm²
Area of the strip = Area of PQRS ˗ Area of ABCD
= 320 cm² ˗ 117 cm²
= 203 cm²

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