Sunday, April 28, 2013

Finding the area of a Trapezoid

Area of a Trapezoid

Here is a link to the video that goes over the two trapezoid area problems.

http://www.youtube.com/watch?v=y0UWiXIaCRw

Let’s first look at where the formula for the area of a trapezoid comes from.

The formula for the area of a trapezoid  equals 1/2h(b1 + b2)  h=height

First a trapezoid has two parallel bases. If you draw a line top vertex straight down it forms a triangle.

 

 

Next, I will rotate the triangle all the way around it forms a rectangle.

 

 Trapezoid to rectangle

 

 

The rectangle has the same area as the original trapezoid and the two bases are equal to each other and is equal to the mid segment. Now when you add the two bases together and multiply by ½ you get an average of the two bases and then multiplying this average by the height. So that is where the formula comes from it the mid segment times the height.

 

Problem 1. Find the area of a trapezoid with a height of 10 units and a base of 12 units and a base of 16 units.

 

 Trapezoid

 

 

Step 1.Plug in 12 and 16 for b1 and b2

  ½ 10 (12 + 16)  

 

 Step 2. ½ (10 * 28)

 

 Step 3.½(280) = 140 units

 

 Problem 2.Find the area of a trapezoid with bases of 5 and 9 and the length of the leg is 4 units. The angle measure is 60◦.

 

 Trapezoid Area

 

 

Step 1.The leg is not your height so you have to find your height.

Since you have a 60◦ angle and a 90◦ angle with the triangle you can take ½ the hypotenuse to get the short leg which equals 2 units ( In a 30,60,90 Triangle the short leg equals 1/2 the hypotenuse)

Next take the length of short leg times 2√3 = the height of the trapezoid

 

 Step 2. Plug in your number in the area formula 

½*2√3 ( 5+9)

 

 Step. 3½ * 2√3 ( 14) = ½ 28√3

 

 Step 4.14√3 = units squared equals the area of the trapezoid