Two adjacent sides of a rhombus form a \(45\)-degree angle. If each side of the rhombus measures 4 cm, what is the area of the rhombus, in square centimeters? Express your answer in simplest radical form.
+2281
Two adjacent sides of a rhombus form a 45-degree angle. If each side of the rhombus measures 4 cm, what is the area of the rhombus, in square centimeters? Express your answer in simplest radical form.
Arearhombus = base • height
A = 4 cm • 2.8284 cm
A = 11.3136 cm2 —–>> Want it in radical form? Well 0.7071 is half the square root of 2.
h = 4 • sqrt(2)/2
h = 2 • sqrt(2)
A = 4 cm • (2 • sqrt(2)) cm
A = 8 • sqrt(2) cm2
How do I know the height? Drop a perpendicular from the top obtuse angle to the side.
The resulting figure is a right triangle, in which you know one side and all of the angles.
Calculate the perpendicular, and that's the height. Draw it and you'll see the following:
sin(45o) = h / 4
h = 4 • sin(45o)
h = 4 • 0.7071
h = 2.8284
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