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abcd is a parallelogram with sides ab=12 cm,bc=10 cm and diagonal ac=16 cm .find the area of the parallelogram also find the di...Asked by Naga
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.
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Answered by
Reiny
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
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