Question

In the given parallelogram ABCD, AB = 10 cm, BC = 15 cm and ∠ABC = 30°. Find the area of ABCD.

Answer 1

Given:

AB = 10 cm

BC = 15 cm

∠ABC = 30°

Find the area of parallelogram ABCD.

Step 1:

Area = Base × Height

BC = 15cm as base.

Drop a perpendicular from point A to base BC.

Height be AP, and form triangle △ABP.

Step 2:

Use trigonometry in triangle △ABP:

sin (30°) = `(AP)/(AB)`

= `1/2 = (AP)/10`

= AP = `10 xx 1/2`

= 5 cm
= Area = Base × Height   ...[calculate the area]

= 15 × 5

= 75 cm²