Question

In the given figure, each square is of unit length

(a) What is the perimeter of the rectangle $ABCD$?

(b) What is the area of the rectangle $ABCD$?

(c) Divide this rectangle into ten parts of equal area by shading squares. (two parts of equal area are shown here)

(d) Find the perimeter of each part which you have divided. Are they all equal?

Answer 1

Given, each side of a square is of unit length.
Figure contains length of $10$ squares and width of $6$ squares.
Length$=10$ units.
Breadth $=6$ units.

(a) The perimeter of the rectangle $ABCD=2($length$+$breadth$)$
$=2(10+6)$
$=2\times 16$
$=32$ units

(b) The area of the rectangle ABCD $=$ Length$\times$ Breadth
$=10\times 6$
$=60$ sq. units

(c) The total area of rectangle $=60$ sq units

Now, we have to divide the rectangle into $10$ equal parts i.e. $\frac{60}{10}=6$ square units,
i.e. we have to take a group of $6-6$ square blocks, which is shown in the figure.

(d) Now, we find the perimeter of each part in above diagram. We know that perimeter of a figure is the total length of its boundary.

$\therefore$ Perimeter of part $E=1+1+1+1+1+1+1+1+1+1+1+1=12$ units

Similarly, we can find the perimeters of remaining $9$ parts, all the parts have same perimeter, i.e. $12$ units

Yes, all the parts have same perimeter.