Construction of a rectangle — lesson. Mathematics State Board, Class 8.

UPSKILL MATH PLUS

Learn Mathematics through our AI based learning portal with the support of our Academic Experts!

Learn more

A rectangle can be constructed using two set of measurements.

The two instances are:

1. When the length and breadth is known.

2. When a side and a diagonal is known.

Method

$1$ : When the length and breadth is known

Let us construct a rectangle with length as

$10$

$cm$ and breadth as

$4$

$cm$ . Let us also calculate the area of the rectangle thus constructed.

Step

$1$ : Draw a rough diagram using the measurements known.

Step

$2$ : Draw a line segment

$AB$ of length

$10$

$cm$ .

Step

$3$ : With

$A$ as centre, draw a perpendicular line.

Step

$4$ : With

$A$ as centre and with

$4$

$cm$ as radius, draw an arc on the perpendicular line and mark the intersection as

$D$ .

Step

$5$ : With

$D$ as centre and with

$10$

$cm$ as radius, draw an arc. Similarly, with

$B$ as centre and with

$4$

$cm$ as radius, cut the existing arc and mark the intersection as

$C$ .

Step

$6$ : Now join

$CD$ and

$BC$ to obtain the desired rectangle.

To find the area of the rectangle:

$\text{Area of the rectangle} = \text{Length} \times \text{Breadth}$

$\text{Area of the rectangle} = l \times b$

We know that,

$l = 10$

$cm$ , and

$b = 4$

$cm$ .

Now,

$\text{Area of the rectangle} = 10 \times 4$

$= 40$

$cm^2$

Method

$2$ : When a side and a diagonal is known

Let us construct rectangle with a side as

$8$

$cm$ and the diagonal as

$10$

$cm$ . Let us also calculate the area of the obtained rectangle.

Step

$1$ : Draw a rough diagram with the known measurements.

Step

$2$ : Draw a line segment

$AB$ of length

$8$

$cm$ .

Step

$3$ : With

$A$ as centre and with

$10$

$cm$ as radius, draw an arc.

Step

$4$ : With

$B$ as centre, draw a perpendicular line until it meets the arc already drawn. Mark the intersection as

$C$ .

Step

$5$ : Measure

$BC$ . In this case,

$BC = 6$

$cm$ , With

$A$ as centre and with

$6$

$cm$ as radius, draw an arc. Similarly, with

$C$ as centre and with

$8$

$cm$ as radius, cut the arc. Mark the intersection as

$D$ .

Step

$6$ : Join

$AD$ and

$CD$ to form the rectangle.

To find the area of the rectangle:

$\text{Area of the rectangle} = \text{Length} \times \text{Breadth}$

$\text{Area of the rectangle} = l \times b$

We know that,

$l = 8$

$cm$ , and

$b = 6$

$cm$ .

Now,

$\text{Area of the rectangle} = 8 \times 6$

$= 48$

$cm^2$

Previous theory

Exit to the topic

Next theory

Send feedback

Did you find an error?

Send it to us!

7. Construction of a rectangle

Theory: