Why do we count the number of unit squares to assign measures for area? Couldn’t we have just used the perimeter Class 8

Why do we count the number of unit squares to assign measures for area? Couldn’t we have just used the perimeter Class 8

Question 1.

Why do we count the number of unit squares to assign measures for area? Couldn’t we have just used the perimeter of a region, i.e., the length of its boundary as a measure of its area? Class 8

Solution:

It is because that area is the measure of the enclosed region by the boundary of a curve (rectangle, triangle, etc.) and perimeter is the measure of that boundary itself.

Question 2.

Find two rectangles that are examples of such regions. If needed, use a grid paper (given at the end of the book) for this. Class 8

Solution:

Perimeter of rectangle I = 2(10 + 5.5)

= 31 cm

Perimeter of rectangle II = 2(8 + 7)

= 30 cm

Area of rectangle I = 10 × 5.5 = 55 sq. cm

So, area of rectangle II = 8 × 7

= 56 cm

So, perimeter of rectangle I > perimeter of rectangle II and area of rectangle I < area of rectangle II.