+357 In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.
+790
In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.
Visualize, or preferably draw, the rhombus, leaning sharply to the right.
Drop a perpendicular from the upper left vertex to the bottom side.
This has made a right triangle with a 20o angle and the hypotenuse 12.
Use trig to find that height.. sin(20o) = height / 12
0.3420 = height / 12
height = 0.3420 • 12 = 4.104
Arearhombus = base • height
Area = 12 • 4.104
Area = 49.25
Note that I rounded the decimal values that I wrote down.
If you calculate it using those values, you'll get 49.248.
I calculated it without rounding, that's where I got 49.25.
.
