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.

JohnyGotchaApples
Nov 30, 2018

#1**+2 **

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.....!!!!

CPhill
Nov 30, 2018