ABCD is a parallelogram with sides AB=12cm,BC=10cm and diagonal Ac=16cm.find the area of parallelogram. Also find the distance between its shorter side.

Answer 1

several ways of doing this:

1. use Heron's formula
split the parallelogram into 2 congruent triangles, then apply using
http://www.mathwarehouse.com/geometry/triangles/area/herons-formula-triangle-area.php

2. Use the cosine law to find the obtuse angle between the two sides 12 and 10
16^2 = 12^2 + 10^2 - 2(12)(10)cosØ

once you have angle Ø
area of ||gram = (12)(10)sinØ

Once you have the area,
use 10 as the base, and let the distance between the two short sides by h, your required altitude.

area = base x height
area = 10h
solve for h, since you have the area from above