Areas of Triangles

Feb 2009
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0
A parallelogram has two adjacent sides of length 4 cm and 6 cm respectively. If the included angle measures 52 degrees, find the area of the parallelogram.

please show all working out.
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
A parallelogram has two adjacent sides of length 4 cm and 6 cm respectively. If the included angle measures 52 degrees, find the area of the parallelogram.

please show all working out.
if \(\displaystyle a\) and \(\displaystyle b\) are the lengths of two adjacent sides of a parallelogram and \(\displaystyle \theta\) is the included angle between those two sides, then the area of the parallelogram is given by

\(\displaystyle
A = a \cdot b \cdot \sin{\theta}
\)
 
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Aug 2010
24
2
../------------|--/
/Theta------- |/
6cm
Area of a parallelogram is given by Base into corresponding altitude..k?
Now, draw perpendicular to one side.. the other side is found out by:
sin theta=opposite leg
--------------
hypotenuse

multiplying sin theta by hypotenuse gives us opposite leg.. which in the case of the triangle with one vertex, theta and altitude.. is the altitude..
so area=a.b.sin theta
=4*6*sin 52
 
Aug 2010
433
115
New Zealand
The area of a triangle is:
\(\displaystyle A = \frac{1}{2}a * b * \sin{C}\)

From your parallelogram, there are 2 identical triangles if you divide your parallelogram in half.
From your information, a = 4, b = 6, C = \(\displaystyle 54^{\circ}\).

There you can work out the area of a triangle, then double it to find the area of your parallelogram.