Question

Construct a parallelogram ABCD with AB = 6 cm, BC = 5.5 cm and $\angle$ ABC = ${80}^o$ and calculate its area.

Answer 1

Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment AB = 6 cm.
Step 3 : At B on $\overline{AB}$ make $\angle$ ABX whose measure is ${80}^o$ .
Step 4 : With B as centre draw an arc of radius 5.5 cm and let it cuts $\overleftrightarrow{BX}$ at C.
Step 5 : With C and A as centres draw arcs of radii 6 cm and 5.5 cm repectively and let them cut at D.
Step 6 : Join $\overline{AD}$ and $\overline{CD}$ . ABCD is the required parallelogram.
Step 7 : From C draw $\overline{CE}\perp \overline{AB}$ and measure the length of CE. CE = h = 5.4 cm. AB = b = 6 cm.
Calculation of area:
In the parallelogram ABCD, b = 6 cm and h = 5.4 cm.
Area of the parallelogram ABCD = b h = 6 *5.4 = 32.4 $c{m}^2$