15.4 Area of Parallelograms and
Trapezoids
Common Core Standards
7.G.4. Know the formulas for the area and circumference of a circle
and use them to solve problems; give an informal derivation of the
relationship between the circumference and area of a circle to write
and solve simple equations for an unknown angle in a figure.
7.G.6. Solve real-world and mathematical problems involving area,
volume and surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and right
prisms.
WARM-UP
Copy and name the quadrilaterals.
1)
2)
3)
4)
Area of Parallelograms and
Trapezoids
How do we find how much space is
inside special quadrilaterals?
base
height
base
base
height
base
NOTES
You can rotate a parallelogram to make any two sides
the bases (bottom and top). The height of a
parallelogram is the straight up distance between the
two bases.
Examples
Find the bases and height of the parallelogram.
10
7
6
10
7
6
NOTES
The formula for the area of a parallelogram is the
same as for rectangles and squares.
Area = bgh
Examples
Find the area of the parallelogram.
11
10 in
9
7
11
5.7 in
10 in
6 in
NOTES
The bases of a trapezoid are the two parallel sides. The
height of a trapezoid is the straight up distance between
the two bases.
Examples
Find the bases and height of the trapezoid.
5
8.3
8.3
7
11
NOTES
The area of a trapezoid can be found by the formula…
1
Area = (b1 + b2 )gh
2
Examples
Find the area of the trapezoid.
10
8 in
9 in
7
6
14 in
EXAMPLES
Write the correct formula for area above each shape.
12"
18"
10"
10"
6"
6"
24"
Find the areas for the above shapes.
18"
PRACTICE
Find the bases and height of each figure.
13cm
10 cm
8cm
3.5 ft
10 cm
13 cm
3'
2.7'
2.5 ft
Find the area of the
parallelogram.
Find the area of the
trapezoid.
PRACTICE
Find the area.
9 ft
17m
11m
9m
17 m
5 ft
5.2 ft
FINAL QUESTION
Find the area.
6"
9.3"
8"
9"