1. Finding the Area of Trapezoids
Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid.
6.G.A.1

2. I can… Determine the area of trapezoids Self Assessment
5- I can do it without help & teach others.
4- I can do this with no help, but I don’t know if I can explain it.
3- I can do this with a little help.
2- I can do this with a lot of help!
1- I don’t have a clue.

3. Finding the Area of Trapezoids
Here is a trapezoid. Let’s find the area of this trapezoid.
To help, let’s use this grid so that we can see square units.
To help, let’s use this grid so that we can see square units.
Here is a trapezoid. Let’s find the area of this trapezoid.

4. Finding the Area of Trapezoids
8 square units
3 square units
1 square unit
Let’s decompose this trapezoid into shapes that we can easily work with.
Here is a triangle.
This rectangle has an area of 6 square units. What is the area of the triangle?
3 square units
Here is another triangle.
This rectangle has an area of 2 square units. What is the area of the triangle?
1 square unit
And, here is a square.
What is the area of the square?
4 square units
Now, to find the area of the whole trapezoid, let’s find the sum of all the parts.
What is 3 square units plus …
… 1 square unit plus …
… 4 square units?
8 square units! The area of this trapezoid is 8 square units.
4 square units
What is 3 square units plus …
Now, to find the area of the whole trapezoid, let’s find the sum of all the parts.
8 square units! The area of this trapezoid is 8 square units.
4 square units
… 4 square units?
… 1 square unit plus …
1 square unit
This rectangle has an area of 6 square units. What is the area of the triangle?
Here is a triangle.
Let’s decompose this trapezoid into shapes that we can easily work with.
3 square units
Here is another triangle.
And, here is a square.
This rectangle has an area of 2 square units. What is the area of the triangle?
What is the area of the square?

5. Finding the Area of Trapezoids
14 square units
Here’s another trapezoid. Let’s decompose it into shapes we can easily work with.
Here is a triangle.
This rectangle has an area of 8 square units. What is the area of the triangle?
4 square units
Here is another triangle.
This rectangle has an area of 4 square units. What is the area of the triangle?
2 square units
And, here is a rectangle.
What is the area of the rectangle?
8 square units
Now, to find the area of the whole trapezoid, let’s find the sum of all the parts.
What is 4 square units plus …
… 2 square units plus …
… 8 square units?
14 square units! The area of this trapezoid is 14 square units.
4 square units
2 square units
8 square units
Now, to find the area of the whole trapezoid, let’s find the sum of all the parts.
What is 4 square units plus …
14 square units! The area of this trapezoid is 14 square units.
8 square units
… 8 square units?
… 2 square units plus …
2 square units
This rectangle has an area of 8 square units. What is the area of the triangle?
Here is a triangle.
Here’s another trapezoid. Let’s decompose it into shapes we can easily work with.
4 square units
Here is another triangle.
And, here is a rectangle.
This rectangle has an area of 4 square units. What is the area of the triangle?
What is the area of the rectangle?

6. Finding the Area of Trapezoids
13 square units
5 square units
6 square units
2 square units
Here’s another trapezoid. Let’s decompose it into shapes we can easily work with.
Here is a triangle.
This rectangle has an area of 10 square units. What is the area of the triangle?
5 square units
Here is another triangle.
This rectangle has an area of 4 square units. What is the area of the triangle?
2 square units
And, here is a rectangle.
What is the area of the rectangle?
6 square units
Now, to find the area of the whole trapezoid, let’s find the sum of all the parts.
What is 5 square units plus …
… 2 square units plus …
… 6 square units?
13 square units! The area of this trapezoid is 13 square units.
What is 5 square units plus …
Now, to find the area of the whole trapezoid, let’s find the sum of all the parts.
13 square units! The area of this trapezoid is 13 square units.
6 square units
… 6 square units?
… 2 square units plus …
2 square units
This rectangle has an area of 10 square units. What is the area of the triangle?
Here is a triangle.
Here’s another trapezoid. Let’s decompose it into shapes we can easily work with.
5 square units
Here is another triangle.
And, here is a rectangle.
This rectangle has an area of 4 square units. What is the area of the triangle?
What is the area of the rectangle?

7. Finding the Area of Trapezoids
Here’s another trapezoid. Let’s decompose it into shapes we can easily work with.
Let’s begin with this triangle.
What is the area of the triangle?
12 square units
Here is another triangle.
3 square units
And, here is a rectangle.
What is the area of the rectangle?
24 square units
Let’s find the sum of the three parts.
What is 12 square units plus …
… 3 square units plus …
… 24 square units?
39 square units! The area of this trapezoid is 39 square units.
39 square units
12 square units
24 square units
3 square units
What is 12 square units plus …
Let’s find the sum of the three parts.
39 square units! The area of this trapezoid is 39 square units.
24 square units
… 24 square units?
… 3 square units plus …
3 square units
What is the area of the triangle?
Let’s begin with this triangle.
Here’s another trapezoid. Let’s decompose it into shapes we can easily work with.
12 square units
Here is another triangle.
And, here is a rectangle.
What is the area of the triangle?
What is the area of the rectangle?

8. Area of a Trapezoid = ½ (b1 + b2) × Height
Finding the Area of Trapezoids
Area of a Trapezoid = ½ (b1 + b2) × Height
½ (9 + 5) • 4
½ (14) • 4
7 • 4
Area = 28 square units 28
5 units
The formula for the area of a trapezoid is ½ the sum of base 1 and base 2 multiplied by the height.
Let’s use this trapezoid to illustrate.
This is base 1 – it is the base we are familiar with.
This parallel side is base 2.
What is the sum of these bases? 14
The formula asks for half of the sum of the bases.
What is half of 14? 7
Next, we need to multiply by the height.
The height of this trapezoid is 4 units.
What is 7 x 4? 28
So, the area of this trapezoid is 28 square units.
4 units
9 units
The height of this trapezoid is 4 units.
What is 7 x 4? 28
Next, we need to multiply by the height.
So, the area of this trapezoid is 28 square units. 14
This is base 1 – it is the base we are familiar with.
Let’s use this trapezoid to illustrate.
The formula for the area of a trapezoid is ½ the sum of base 1 and base 2 multiplied by the height.
This parallel side is base 2.
What is the sum of these bases?
What is half of 14?
The formula asks for half of the sum of the bases. 7

9. Area of a Trapezoid = ½ (b1 + b2) × Height
Finding the Area of Trapezoids
Area of a Trapezoid = ½ (b1 + b2) × Height 14 2 =
9 + 5 = 14 7
7 × 4 = 28
Area = 28 square units
Let’s connect the answer from the formula to the answer we find by decomposing the trapezoid.
What is the area of this triangle?
2 square units
6 square units
What is the area of the rectangle?
20 square units
What is the sum of all the parts?
28 square units
2 square units
20 square units
6 square units
What is the sum of all the parts?
28 square units
20 square units
6 square units
Let’s connect the answer from the formula to the answer we find by decomposing the trapezoid.
What is the area of this triangle?
2 square units
What is the area of this triangle?
What is the area of the rectangle?

10. Area of a Trapezoid = ½ (b1 + b2) × Height
Finding the Area of Trapezoids
Area of a Trapezoid = ½ (b1 + b2) × Height
½ (11 + 5) • 3
½ (16) • 3
8 • 3
Area = 24 square units 24
5 units
Now, let’s find the area of this trapezoid using the formula.
This is base 1 – it is the base we are familiar with.
This parallel side is base 2.
What is the sum of these bases? 16
The formula asks for half of the sum of the bases.
What is half of 16? 8
Next, we need to multiply by the height.
The height of this trapezoid is 3 units.
What is 8 x 3? 24
So, the area of this trapezoid is 24 square units.
3 units
11 units 24
What is 8 x 3?
So, the area of this trapezoid is 24 square units.
What is half of 16?
This parallel side is base 2.
This is base 1 – it is the base we are familiar with.
Now, let’s find the area of this trapezoid using the formula.
What is the sum of these bases? 16
Next, we need to multiply by the height. 8
The formula asks for half of the sum of the bases.
The height of this trapezoid is 3 units.

11. Area of a Trapezoid = ½ (b1 + b2) × Height
Finding the Area of Trapezoids
Area of a Trapezoid = ½ (b1 + b2) × Height 16 2 = = 16 8
8 × 3 = 24
Area = 24 square units
Let’s connect the answer from the formula to the answer we find by decomposing the trapezoid.
What is the area of this triangle?
3 square units
6 square units
What is the area of the rectangle?
15 square units
What is the sum of all the parts?
24 square units
3 square units
15 square units
6 square units
What is the area of the rectangle?
3 square units
What is the area of this triangle?
Let’s connect the answer from the formula to the answer we find by decomposing the trapezoid.
What is the area of this triangle?
6 square units
What is the sum of all the parts?
15 square units
24 square units

12. Area of a Trapezoid = ½ (b1 + b2) × Height
Finding the Area of Trapezoids
Area of a Trapezoid = ½ (b1 + b2) × Height
4 cm
½ (6 + 4) • 3
½ (10) • 3
5 • 3
3 cm 15
Let’s use the formula to find the area of this trapezoid.
What is the measurement of base 1?
6 cm
What is the measurement of base 2?
4 cm
What is the sum of the bases? 10
We need to find half of the sum of the bases.
What is half of 10? 5
Now, we need to multiply by the height.
What is the height?
3 cm
So, what is 5 x 3? 15
So, the area of this trapezoid is 15 square cm.
6 cm
15 square cm
So, what is 5 x 3?
What is the height?
So, the area of this trapezoid is 15 square cm.
3 cm 15
What is the measurement of base 1?
We need to find half of the sum of the bases. 10
What is the sum of the bases?
Let’s use the formula to find the area of this trapezoid.
What is half of 10? 5
4 cm
6 cm
Now, we need to multiply by the height.
What is the measurement of base 2?

13. Area of a Trapezoid = ½ (b1 + b2) × Height
Finding the Area of Trapezoids
Area of a Trapezoid = ½ (b1 + b2) × Height
7 m
½ (11 + 7) • 5
½ (18) • 5
5 m
9 • 5 45
Let’s use the formula to find the area of this trapezoid.
What is the measurement of base 1?
11 meters
What is the measurement of base 2?
7 meters
What is the sum of the bases? 18
We need to find half of the sum of the bases.
What is half of 18? 9
Now, we need to multiply by the height.
What is the height?
5 meters
So, what is 9 x 5? 45
So, the area of this trapezoid is 45 square meters.
11 m
45 square m
What is the height?
So, what is 9 x 5? 45
5 meters
So, the area of this trapezoid is 45 square meters.
What is the measurement of base 1?
We need to find half of the sum of the bases. 18
What is the sum of the bases?
Let’s use the formula to find the area of this trapezoid.
What is half of 18? 9
7 meters
11 meters
Now, we need to multiply by the height.
What is the measurement of base 2?

14. Area of a Trapezoid = ½ (b1 + b2) × Height
Finding the Area of Trapezoids
Area of a Trapezoid = ½ (b1 + b2) × Height
8 km
½ (8 + 14) • 9
9 km
½ (22) • 9
11 • 9
Let’s use the formula to find the area of this trapezoid.
What is the measurement of base 1?
14 km
What is the measurement of base 2?
8 km
What is the sum of the bases? 22
We need to find half of the sum of the bases.
What is half of 22? 11
Now, we need to multiply by the height.
What is the height?
9 km
So, what is 11 x 9? 99
So, the area of this trapezoid is 99 square km. 99
14 km
99 square km
What is the height?
So, what is 11 x 9?
9 km 99
So, the area of this trapezoid is 99 square km.
What is the measurement of base 1?
We need to find half of the sum of the bases. 22
What is the sum of the bases?
Let’s use the formula to find the area of this trapezoid.
What is half of 22? 11
8 km
14 km
Now, we need to multiply by the height.
What is the measurement of base 2?

15. Finding the Area of Trapezoids
Your Turn…

16. What is the area of the trapezoid?
Finding the Area of Trapezoids
What is the area of the trapezoid?
3 feet
½ (5 + 3) • 2
½ (8) • 2
2 feet
4 • 2 8
5 feet
8 square feet

17. What is the area of the trapezoid?
Finding the Area of Trapezoids
What is the area of the trapezoid?
6 cm
½ (10 + 6) • 4
½ (16) • 4
4 cm
8 • 4 32
10 cm
32 square cm

18. What is the area of the trapezoid?
Finding the Area of Trapezoids
What is the area of the trapezoid?
½ (12 + 6) • 3
6 km
½ (18) • 3
9 • 3
3 km 27
12 km
27 square km

19. What is the area of the trapezoid?
Finding the Area of Trapezoids
What is the area of the trapezoid?
½ ( ) • 35
50 cm
½ (200) • 35
100 • 35
35 cm
3,500
150 cm
3,500 square cm

20. I can… Determine the area of trapezoids Self Assessment
5- I can do it without help & teach others.
4- I can do this with no help, but I don’t know if I can explain it.
3- I can do this with a little help.
2- I can do this with a lot of help!
1- I don’t have a clue.

21. Area = (base 1 + base 2)•height Area = ½ (base 1 + base 2)•height
Area of a Trapezoid
10.2 Notes
Area = (base 1 + base 2)•height 2
Area = ½ (base 1 + base 2)•height b2 b1 h
Copy the equation (don’t just solve in your head)
Substitute the numbers for the variables
Solve