Question

Construct a quadrilateral $DEAR$ with $DE=6cm,EA=5cm,AR=5.5cm,RD=5.2cm$ and $DA=10cm$. Also find its area.

Answer 1

Given:
$\begin{array}{cc}& DE=6cm,EA=5cm,AR=5.5cm\\ & RD=5.2cm\text{and a diagonal}\\ & DA=10cm\end{array}$
Steps:
1. Draw a line segment $DE=6cm$.
2. With $D$ and $E$ as centres, draw arcs of radii $10cm$ and $5cm$ respectively and let them cut at $A$.
3. Join $DA$ and $EA$.
4. With $D$ and $A$ as centres, draw arcs of radii $5.2cm$ and $5.5cm$ respectively and let them cut at $R$.
5. Join $DR$ and $AR$.
6. DEAR is the required quadrilateral.
Calculation of Area:
$\begin{array}{cc}\text{Area of the quadrilateral}DEAR& =\frac{1}{2}\times d\times (h_1+h_2)\text{sq. units}\\ & =\frac{1}{2}\times 10\times (1.9+2.3)=5\times 4.2=21{cm}^2\end{array}$