2. To find area of trapezium we will first
review
The Area of a Triangle & Parallelogram.
Then we are going to discover the
Area of a Trapezium.
3. Given the formula for
area of a rectangle, we are going to
use that information to discover the
formula for the area of a triangle.
4. Given a right triangle
Make a similar triangle and
flip it and put them both next
to each other.
What polygon is
this?
A Rectangle
5. We can use the formula for area of a rectangle
to find the formula for area of a triangle.
b
A=
2
hA=b h
Two triangles make
one rectangle.
We want to find half of
the area of the rectangle.
base
height
b
h
We divide 2 since we are
finding half of the area
6. base
height
h
This holds true for any triangle
b h
A=
2
Notice when we put two right triangles together it made
a rectangle. When we put two isosceles triangle
together it made a parallelogram. We are still finding
half the area so we divide by 2.
7. A triangle is half the area of a rectangle.
To find the area of a triangle, you use the
rectangle formula (base times height)
and divide it in half.
A = base •height
2
5 m
12 m
13 m
A = 5 • 12
2
= 30 m2
A=
1
2
bhbh
A=
2
8. Given the formula for
area of a triangle and the formula
for area of a parallelogram we are
going to use that information to
discover the formula for the
area of a trapezoid
9. This trapezoid is regular.
Regular Trapezoid
This trapezoid is an irregular trapezoid.
Irregular Trapezoid
Also known as an
Isosceles Trapezoid
10. b2
b1
h
Copy that trapezoid, flip it over,
and put it next to the original
b2
b1
h
Give the height, base 1 & base 2
(b1 + b2)
What polygon
is it now?
Parallelogram
11. Notice that the trapezium is half the area of the
parallelogram.
(b1 + b2)
h
Given our original trapezoidput together with a similar
flipped trapezoid, we found it made a parallelogram.
We are going to use the area of a parallelogram
to find the area of a trapezium.
It takes two trapezium to make
one parallelogram.
12. (b1 + b2)
h
Parallelogram Trapezoid
Notice that the trapezoid is half the area
of the parallelogram. How do we find
half the area?
2
A = (b1 + b2) * h
Hint: Think of
area of a triangle
A= b*h
13. Area of Trapezoid2 in
6 in
3 in
= 12
2
A = (b1 + b2) •h
A=(2+6)*3
2
=
(8)*3
2
=
24
2
14. 4
5
7
6
Here is another
way to look at the
trapezoid formula.
Instead of dividing
by 2, multiply by ½
A=1(b1 + b2)*h
2
A=1(5+7)*4
2
A=1(12)*4
2
A=6*4
=24