Master the 7 pillars of school success
Improve your grades and lower your stress
Common Core Standard 7.G.6
Area of a trapezoid with 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.
Video tutorial covering, "How to find the area of a trapezoid"
Step by step instructions for finding the area of a trapezoid
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
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:
Area of a Trapezoid
How to find the area of a trapezoid
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
4
You may also enjoy
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◦.
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)
b1
b2
Formula for the area of a trapezoid equals 1/2h (b1+b2)
h = height, b1 =base, b2 =base
h
What is a trapezoid