Question

Amita wants to make rectangular cards measuring 8 cm$\times$5 cm. She has a square chart paper of side 60 cm. How many complete cards can she make from this chart? What area of the chart paper will be left ?
[4 marks]

Answer 1

Let ABCD be a square chart of side 60 cm.
We have to cut out rectangular cards measuring 8 cm$\times$5 cm out of this chart.

Now, if we chart along AB as shown in the figure, then we can cut 12 rectangular cards from one row i.e. $\frac{60cm}{5cm}$ = 12
[0.5 mark]

Similarly, we can cut 7 rows with 12 rectangular cards in each as in $\frac{56cm}{8cm}$ = 7
[0.5 mark]
Hence, total number of rectangular cards =12 × 7 = 84
[0.5 mark]

Now, Area of whole sheet = 60 cm × 60 cm
=3600 $c{m}^2$
[0.5 mark]

Area of one rectangular card = (8 cm × 5 cm)
= 40 $c{m}^2$
Thus, area of 84 rectangular cards = 84 × 40 $c{m}^2$
= 3360 $c{m}^2$
[1 mark]

Now, area of the left part = Area of whole sheet - Area of 84 rectangular cards
⇒ ( 3600 $c{m}^2$ -3360 $c{m}^2$ ) = 240 $c{m}^2$
Hence, the area left on the chart paper is 240 $c{m}^2$.
[1 mark]