+159 1. What is the perimeter of the trapezoid shown?
2. What is the area of the trapezoid shown? Express your answer in simplest exact form.
+129852 If we draw a perpendicular from the top right vertex to the lower base......we will create a 30-60-90 right triangle.....the right side of the trapezoid will be the hypotenuse = 2
And the height of this triangle = side opposite the 60” angle = sqrt(3) = height of trapezoid
The angle opposite the 30 degree angle at the top = (1/2)hypotenuse = 1
Using symmetry....we have the same situation on the left side of the trapezoid
So...the perimeter = 2 units on the top base.....2 + 1 + 1 = 4 units on the bottom base
And 2(2) = 4 units on the sides
So......the perimeter is 2 + 4 + 2(2) = 10 units
Area = (1/2) height of trapezoid ( sum of base lengths) =
(1/2)sqrt(3) * ( 2 + 4) =
(1/2) sqrt (3) (6) =
(3)sqrt (3) units^2
THANKS TO EP FOR POINTING OUT MY ERROR IN THE HEIGHT CALCULATION.....!!!!
