Construct a quadrilateral NICE with $N I = 4.5 c m, I C = 4.3 c m, N E = 3.5 c m, N C = 5.5 c m$ and $I E = 5 c m$ . Also find its area.

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Solution

Given:
$N I = 4.5 c m, I C = 4.3 c m$ ,
$N E = 3.5 c m$ and two diagonals,
$N C = 5.5 c m$ and $I E = 5 c m$
Steps:
1. Draw a line segment $N I = 4.5 c m$ .
2. With $N$ and $I$ as centres, draw arcs of radii $5.5 c m$ and $4.3 c m$ respectively and let them cut at $C$ .
3. Join $N C$ and IC.
4. With $N$ and $I$ as centres, draw arcs of radii $3.5 c m$ and $5 c m$ respectively and let them cut at $E$ .
5. Join $N E, I E$ and $C E$
6. NICE is the required quadrilateral.
Calculation of Area:
Area of the quadrilateral NICE $= \frac{1}{2} \times d \times (h_{1} + h_{2})$ sq. units
$\begin{matrix} = \frac{1}{2} \times 5 \times (2.4 + 3.1) = 2.5 \times 5.5 = 13.75 {c m}^{2} \end{matrix}$

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