Posted by **mohib** on Monday, December 19, 2011 at 4:55pm.

In rectangle ABCD, shown here, ACB measures 30° and. CD = 40 mm. What is the area of rectangle ABCD? Express your answer as a decimal to the nearest tenth

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**Reiny**, Monday, December 19, 2011 at 6:38pm
So we have a right-angled triangle with angles 30-60-90

The sides of such a triangle are in the ration 1 : √3 : 2

So ours must have sides 40,40√3, and 80

making the base 80

Area = 40(40√3) = 1600√3 = appr. 2771.3

or

tan30 =AB/BC

BC = 40/tan30 = 69.282

area = 40(69.282) = appr. 2771.3

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