Mathematics
In the figure (iii) given below, from a 24 cm × 24 cm piece of cardboard, a block in the shape of letter M is cut off. Find the area of the cardboard left over, all measurements are in centimetres.
Answer
From figure,
Area of rectangle (I) = length × breadth
= 24 × 6
= 144 cm2.
Area of rectangle (II) = length × breadth
= 24 × 6
= 144 cm2.
Area of parallelogram (III) = base × height
= 8 × 6
= 48 cm2.
Area of parallelogram (IV) = base × height
= 8 × 6
= 48 cm2.
Area of figure M = Area of rectangle (I) + Area of rectangle (II) + Area of parallelogram (III) + Area of parallelogram (IV)
= 144 + 144 + 48 + 48
= 384 cm2.
Area of cardboard = 24 × 24
= 576 cm2.
Area of cardboard left = Area of cardboard - Area of figure M
= 576 - 384
= 192 cm2.
Hence, area of cardboard left = 192 cm2.
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