Question
Two adjacent sides of a parallelogram have lengths $a$ and $b$ and the angle between these two sides is $\theta .$ Express the area of the parallelogram in terms of $a$$b$ and $\theta$.
Step 1
This divides the parallelogram into two triangles. Show more…
Show all steps
Your feedback will help us improve your experience
Julian Wong and 72 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Area of a Parallelogram. Prove that the area of a parallelogram is the product of two adjacent sides and the sine of the included angle.
Applications of Trigonometry
The Law of Sines
If the lengths of two adjacent sides of a parallelogram are $a$ and $b,$ and if the acute angle formed by these two sides is $\theta,$ show that the product of the lengths of the two diagonals is given by the expression $$ \sqrt{\left(a^{2}+b^{2}\right)^{2}-4 a^{2} b^{2} \cos ^{2} \theta} $$
Additional Topics in Trigonometry
The Law of Sines and the Law of Cosines
Let $A B C D$ be a parallelogram with $A B=c, B C=a,$ and $\mathrm{m} \angle B=\theta .$ a. Write a formula for the area of parallelogram $A B C D$ in terms of $c, a,$ and $\theta$ . b. For what value of $\theta$ does parallelogram $A B C D$ have the greatest area?
TRIGONOMETRIC APPLICATIONS
Area of a Triangle
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD