Question

Construct a quadrilateral $VABN$ where $VA=7cm,AB=8cm,BN=10cm,AN=12cm$ and $VB=11cm.$

The perimeter (in cm.) of $\square VABN$ is

Answer 1

1. Draw a line segment $BV=11cm$.

2. With $7cm$ as radius, draw an arc from $V$.

3. Similarly, with radius as $8$ cm from $B$, cut the arc just drawn.

4. They will intersect at $A$. Join $AB$ and $VA$.

5. With $10cm$ as radius, draw an arc from $B$. Similarly, with radius as $12cm$ from $A$, cut the arc just drawn.

6. They will intersect at $N$. Join $AN$ and $BN$.

7. Join $NV$.

8. $ABNV$ is the required quadrilateral.

9. Using ruler, we can measure length of $VN$, which comes out to be $5cm$.

10. Perimeter of the $\square VABN$ is $VA+AB+BN+NV=7+8+10+5cm=30cm$