An increase in perimeter of a figure always increases the area of the figure. Is the given statement true or false?
Solution:
Given, an increase in perimeter of a figure always increases the area of the figure.
We have to determine if the given statement is true or false.
Area is the amount of space occupied by a two-dimensional figure.
Perimeter is the total length of the boundary of any closed shape.
In figure (2), a hole is made in the circle.
Now, there are two circumference of circle since there is one more edge
So, the perimeter of (2) will be greater than (1) but the area of (2) will be smaller than (1).
Therefore, an increase in perimeter of a figure does not always increase the area of the figure.
✦ Try This: Compare figure A and B and comment about their area and perimeter.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 70
An increase in perimeter of a figure always increases the area of the figure. Is the given statement true or false?
Summary:
The given statement, “An increase in perimeter of a figure always increases the area of the figure” is false.
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