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Common Core Standard   7.G.6

Area of a trapezoid with diagonals

trapezoid with perpendicular diagonals
Video answers these questions
Why use the formula 1/2h(b1+b2) to find the area of a trapezoid?

What is the area of a trapezoid with a height of 10 units, and sides of 12 and 16 units

What is the area of a trapezoid with sides of 4,5, and 9 units?
In order to solve this triangle you have to find the height of the trapezoid.
Step by step instructions for finding the area of a trapezoid
area of a trapezpoid gif
Find the area of trapezoid ABCD that has diagonals of 6 and 8 units.

Use the formula   d1*d2/2

6*8/2 = 48/2 = 24 units squared 
D
C
B
A
​d2
​d1
d1*d2/2
Caution: You can find the area of a trapezoid using the diagonals, but the diagonals must cross and form perpendicular lines.
This creates four right angles, and you can use the formula:   
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Area of a Trapezoid

How to find the area of a trapezoid

trapezoid 12 x16
trapezoid 5x4x9
trapezoid 5x5x4x9
Step 2. To find the long leg length (which will equal the trapezoid height) apply the 
rules of a 30 60 90 triangle, therefore the long leg ( height) equals  short leg x √3 

  • The short leg is 1/2 the hypotenuse
  • The hypotenuse is always opposite the right angle therefore equals 4 units
  • Short leg equals 1/2 x 4=2 units
  • Long leg equals the short leg√3, 
  • Plug in the short leg   2√3 =height ​

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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◦.

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Step 1. Please don't make the mistake of using the side length as your height. 
The height in this trapezoid creates a 30 60 90 triangle. The height becomes the long leg of a 30 60 90 triangle. 
Step 3. Plug the height into the  area formula of a trapezoid   1/2h (b1 + b2)

  • 1/2*2√3 ( 5+9)

Step 4. ½ * 2√3 ( 14) = ½ 28√3

Step 5. 14√3 = units squared equals the area of the trapezoid
Find the area of a trapezoid with a height of 10 units, a base of 12 units and a base of 16 units.


Step 1. Plug in 12 and 16 for b1 and b2 and 10 for the height. 
  ½ 10 (12 + 16)  

Step 2. ½ (10 * 28)

Step 3. ½(280) = 140 units

​A trapezoid is a four sided polygon with one pair of parallel sides. Area is a measure of the number of square units found inside the trapezoid. Area is a two dimensional measure so it is always squared. The height of the trapezoid is perpendicular to the two parallel bases. One common mistake made when calculating the area of a trapezoid is to use the side length as the height. Again, the height is measured as a line perpendicular to the two parallel bases.

The area of a trapezoid may be found using the formula 1/2h(b1+b2) 


green trapezoid
b 
b2 
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​Formula for the area of a trapezoid equals 1/2h (b1+b2)      
                                                                                    h = height, b1 =base,  b2 =base
h
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What is a trapezoid