Quadrilaterals
• A quadrilateral is a geometric figure that is made up of four line segments, called sides, that intersect only at their endpoints.
Special Quadrilaterals
• Trapezoid– A quadrilateral with exactly
1 pair of parallel sides.
• Parallelogram– A quadrilateral with 2 pairs
of parallel sides.
To find the area of a parallelogram, you always multiply the base and the height.
So, Area = base x height or A = bh
Remember: The height is the line segment that is perpendicular to the
base and creates a right angle.12 in
10 in
10 in
What is the area of this parallelogr
am?Area = base x height
A = (10)(10)A = 100 in²
Your TurnFind the area and perimeter of the
parallelogram.
24 cm
12 cm
A=bhA= 12(24)A=288 cm²
14 cm
P = 12+12+14+14
P = 52 cm
Area of a Triangle
1
2
Area of parallelogram = base x heightArea of triangle = base x height
2
1
Area = bh
2
1
Finding the Area of a Triangle
1. Write the formula for area of a triangle.
2. Substitute in values.
3. Simplify.
11 ft
23 ft
2
1
A= bh
2
1
A= (23)(11)
A= 126.5 ft²
You try!Find the area and perimeter of the
triangle.
17 m
13.4 m A= bh
A= (17)(13.4)
A= 113.9 m²
2
1
2
1
20 m 15 m
P = 20+15+17P = 52 m
Given the formula for the area of a parallelogram we are going to use that information to discover the
formula for the area of a trapezoid.
Watch carefully not to miss it!
Notice that the trapezoid is half the area of the parallelogram.
(b1 + b2)
h
Copy the trapezoid, flip it over, and put it next to the original. It makes a parallelogram.
We are going to use the area of a parallelogram to find the area of a trapezoid. It takes two trapezoids to make one parallelogram.
(b1 + b2)
h
Parallelogram
Trapezoid
Notice that the trapezoid is half the area of the parallelogram. How do we find
half the area?
A = (b1 + b2) • h
Hint: Think of area of a triangle.
hbA 2
1
Area of Trapezoid
2 in
6 in
3 in A = (b1 + b2) • h
4 in
2
1
A = (2 + 6) • 32
1
A = (8) • 32
1
A = 4 • 3A = 12 in²
4 in
Perimeter of Trapezoid
P = 4 + 4 + 2 + 6P = 16 in
Area of Trapezoid
3 m
8 m
4 m 5 m A = (b1 + b2) • h
2
1
A = (3 + 8) • 42
1
A = (11) • 42
1
A = (44)
A = 22 m²
2
1
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