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
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
To find the area of rectangle ABCD, we need to know the length and width of the rectangle. However, without any additional information, we cannot determine the length and width directly from the given information.
If you have a diagram or more details about the rectangle (like the measure of another angle or a ratio between the sides), please provide that additional information so that I can assist you in finding the area of the rectangle.