Question

Construct a parallelogram ABCD with AB = 8 cm, AD = 7 cm and BD = 9 cmand find its area.

Answer 1

Given:
AB = 8 cm, AD = 7 cm and BD = 9 cm.
Steps for construction
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment AB = 8 cm.
Step 3 : With A and B as centres draw arcs of radii 7 cm and 9 cm respectively and let them cut at D.
Step 4 : Join $\overline{AD}$ and $\overline{BD}$ .
Step 5 : With B and D as centres draw arcs of radii 7 cm and 8 cm respectively and let them cut at C.
Step 6 : Join $\overline{CD}$ and $\overline{BC}$ . ABCD is the required parallelogram.
Step 7 : From D draw $\overline{DE}\perp \overline{AB}$ and measure the length of DE. DE = h = 6.7 cm. AB = DC= b = 8 cm
Calculation of area:
In the parallelogram ABCD, b = 8 cm and h = 6.7 cm.
Area of the parallelogram ABCD = b h
= 8* 6.7 = 53.6 $c{m}^2$ .