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5. Construction of a quadrilateral when the length of the 4 sides and the diagonal are given

Depending upon the lengths of the sides and diagonal, create a triangle of $PQR$ based on $SSS$ construction.

Make an arc (point $S$ ) at a certain distance from $P$ .

Make an arc at a certain distance from point $R$ on the earlier arc on $S$ . Name the two points intersection as $S$ .

$P$ and $R$ join $S$ . The quadrilateral $PQRS$ will be achieved.

Example:

Construct a quadrilateral

$ABCD$ with the following measurements.

$AB =$

$4.5 cm$ ,

$BC =$

$5.5 cm$ ,

$CD = 4cm$ ,

$AD = 6cm$ ,

$AC = 7cm$ .

Step 1:Draw side

$BC = 5.5 cm$ and cut arcs above it from

$B$ (

$4.5 cm$ ) and

$C$ (

$7 cm$ ). Mark the intersection as

$A$ . Join

$AB$ and

$AC$ .

Step 2: Draw and arc from

$A$ equal to

$6 cm$ which is the length of

$AD$ .

Step 3: Draw and arc from

$C$ equal to

$4 cm$ which is the length of

$CD$ . Mark the intersection as

$D$ and join

$AD$ and

$CD$ .

Thus, the

$ABCD$ is a required quadrilateral.

Calculate Area of quadrilateral:

Area of the quadrilateral

$ABCD$

$=$

$\frac {1}{2}$

$\times$

$d$

$\times$

$h_1 + h_2$ sq. units

$=$

$\frac{1}{2} × 10 (1.9 +2.3)$

$=$

$5\times 4.2$

$=$

$21 cm²$ .

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5. Construction of a quadrilateral when the length of the 4 sides and the diagonal are given

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