Question

Construct the following quadrilateral: Quadrilateral $\text{LIFT}$. $\text{LI = 4 cm, IF = 3 cm, TL = 2.5 cm, LF = 4.5 cm, IT = 4 cm}$

Answer 1

Let's draw a rough sketch of a quadrilateral $\text{LIFT}$, to get an idea about the parallelogram -

$$\begin{gathered} \text{LI = 4 cm,} \\ \text{IF = 3 cm,} \\ \text{TL = 2.5 cm,} \\ \text{LF = 4.5 cm,} \\ \text{IT = 4 cm} \end{gathered}$$

Let's construct the quadrilateral$\text{LIFT}$ using the information given in the question -

Step 1: Draw a line segment$\text{LI = 4 cm}$, then take an arc of radius $\text{4 cm}$ on the compass & cut an arc from the point $\text{I}$, then change the radius to $\text{2.5 cm}$ and cut another arc from point$\text{L}$ which bisect each other at point$\text{T}$ -

Step 2: Join $\text{LT \& IT}$, then take an arc of radius $\text{4.5 cm}$ on the compass & cut an arc from point$\text{L}$, then change the radius to $\text{3 cm}$ and cut another arc from point $\text{I}$ which intersect each other at point$\text{F}$ and then join $\text{LF and IF}$ -

Step 3: Join $\text{TF}$ to get the required quadrilateral -

Hence, $\text{LIFT}$is the required quadrilateral.