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# rhombus

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In a rhombus, all the side lengths are \$12,\$ and one of the angles is equal to \$150^\circ.\$  Find the area of the rhombus.

Dec 31, 2023

#1
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In a rhombus, all the side lengths are \$12,\$ and one of the angles is equal to \$150^\circ.\$  Find the area of the rhombus.

Area  =  base • height

Area  =  12 • 6

Area  =  72

Where did that value for the height come from?

One of the angles is 150o so the one next to it is 30o.

Drop a perpendicular from the 150o angle at the top vertex.

Use trig.  You know the hypotenuse is 12 and the angle is 30o.

sin(30) = h / 12   (opposite over hypotenuse)

0.5 = h / 12   ====>  h = 6

.

Jan 1, 2024

#1
+1014
+1

In a rhombus, all the side lengths are \$12,\$ and one of the angles is equal to \$150^\circ.\$  Find the area of the rhombus.

Area  =  base • height

Area  =  12 • 6

Area  =  72

Where did that value for the height come from?

One of the angles is 150o so the one next to it is 30o.

Drop a perpendicular from the 150o angle at the top vertex.

Use trig.  You know the hypotenuse is 12 and the angle is 30o.

sin(30) = h / 12   (opposite over hypotenuse)

0.5 = h / 12   ====>  h = 6

.

Bosco Jan 1, 2024