NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - Problems and Solutions

Question 41

Given: Each small square is 1 unit by 1 unit (so its area is 1 sq unit).

Count the sides of rectangle ABCD:
Length = 14 units (14 squares along the long side)
Breadth = 4 units (4 squares along the short side)

(a) Perimeter of ABCD

Formula: ( P = 2(L + B) )

First add: ( L + B = 14 + 4 = 18 )

Now double it: ( P = 2 imes 18 = 36 ) units

Note: If your answer key shows 30 units, that’s a mistake. With 14 and 4, the correct perimeter is 36 units.

(b) Area of ABCD

Formula: ( A = L imes B )

Multiply: ( 14 imes 4 = 56 ) sq units

(c) Divide into 10 equal-area parts

Total area = 56 sq units

Area of each part = ( dfrac{56}{10} = 5.6 ) sq units

Since each small square is 1 sq unit, 5.6 sq units means you cannot use only whole squares for each part.

Easy way: Split the length (14 units) into 10 equal strips.
Each strip has length ( dfrac{14}{10} = 1.4 ) units and the same breadth 4 units.

Check area of one strip: ( 1.4 imes 4 = 5.6 ) sq units (correct)

Shade the strips alternately to show 10 equal parts.

(d) Perimeter of each part — are they all equal?

If you used neat rectangular strips (size ( 1.4 imes 4 )):

Perimeter of one strip: ( P = 2(1.4 + 4) )

First add: ( 1.4 + 4 = 5.4 )

Now double: ( 2 imes 5.4 = 10.8 ) units

All strips are identical rectangles, so their perimeters are equal (10.8 units each).

If, instead, you make different shapes (like zig-zag boundaries around squares), the areas can still be 5.6 sq units but the perimeters will not all be equal. Perimeter depends on the shape of the boundary, not just the area.