Graph of Area vs. Side of a Square

Here we will learn about the graph of area vs. side of a square.

We know that area of a square = (side)². Thus, A = x².

(a) Consider the relation between the area and the side of a square, given by A = x².
Draw a graph of the above function.

(b) From the graph, find the value of A, when x = 4.

Solution:

The given function is A = x².
For different values of x, we get the corresponding value of A.

x= 0 ⇒ A = 0² = 0
x= 1 ⇒ A = 1² = 1
x = 2 ⇒ A = 2² = 4
x = 3 ⇒ A = 3² = 9

x	0	1	2	3
A = x2	0	1	4	9

Thus, we have the points O (0, 0), B (1, 1), C (2, 4) and D (3, 9). 

Plot these points on a graph paper and join them successively to obtain the required graph given below. 

2. Reading off from the graph of area vs. side of a square:

On the x-axis, take the point L at x = 4. 

Draw LP ⊥ x-axis, meeting the given graph at P. 

Clearly, PL = 16 units. 

Therefore, x = 4 ⇒ A = 16. 

Thus, when x = 4 units, then A = 16 sq. units

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Related Concepts:

● Coordinate Graph

● Ordered pair of a Coordinate System

● Plot Ordered Pairs

● Coordinates of a Point

● All Four Quadrants

● Signs of Coordinates

● Find the Coordinates of a Point

● Coordinates of a Point in a Plane

● Plot Points on Co-ordinate Graph

● Graph of Linear Equation

● Simultaneous Equations Graphically

● Graphs of Simple Function

● Graph of Perimeter vs. Length of the Side of a Square

● Graph of Simple Interest vs. Number of Years

● Graph of Distance vs. Time

7th Grade Math Problems

8th Grade Math Practice

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