8-1 Perimeter & Area Rectangles & Parallelograms
Math 8 Mr. Dixon
Any side of a rectangle or parallelogram can be chosen as the base. The height is measured along a line perpendicular to the base. Rectangle
Parallelogram
Height Base
Height Base
Side
Perimeter is the distance around the outside of a figure. To find the perimeter of a figure, add the lengths of all its sides.
Additional Example 1: Finding the Perimeter of Rectangles and Parallelograms Find the perimeter of the figure. 5 P = 14 + 14 + 5 + 5 = 38 units
14
or P = 2b + 2h = 2(14) + 2(5) = 28 + 10 = 38 units
Add all side lengths. Perimeter of rectangle. Substitute 14 for b and 5 for h.
Additional Example 2: Finding the Perimeter of Rectangles and Parallelograms Find the perimeter of the figure. 16
20 P = 16 + 16 + 20 + 20 = 72 units
Add all side lengths.
Area is the number of square units in a figure. A parallelogram can be cut and the cut piece shifted to form a rectangle with the same base length and height as the original parallelogram. So a parallelogram has the same area as a rectangle with the same base length and height.
Helpful Hint The formula for the area of a rectangle can also be written as A = lw.
Additional Example 3: Using a Graph to Find Area Graph the figure with the given vertices. Then find the area of the figure.
(–1, –2), (2, –2), (2, 3), (–1, 3) Area of a rectangle. A = bh Substitute 3 for b and 5 for h. A=3•5 A = 15 units2
Check It Out: Graph the figure with the given vertices. Then find the area of the figure. (–1, –1), (3, –1), (5, 3), (1, 3) y
(1, 3)
(5, 3)
4
(–1, –1) 4 (3, –1)
x
Area of a parallelogram. A = bh Substitute 4 for b and 4 for h. A=4•4 A = 16 units2
Pg. 395 (1 – 7) All; (10 – 16) All; 19 & 20
Calculators may be used.
Show all work to receive full credit.
Any side of a rectangle or parallelogram can be chosen as the base. The height is measured along a line perpendicular to the base. Rectangle
Parallelogram
Height Base
Height Base
Side
Perimeter is the distance around the outside of a figure. To find the perimeter of a figure, add the lengths of all its sides.
Additional Example 1: Finding the Perimeter of Rectangles and Parallelograms Find the perimeter of the figure. 5 P = 14 + 14 + 5 + 5 = 38 units
14
or P = 2b + 2h = 2(14) + 2(5) = 28 + 10 = 38 units
Add all side lengths. Perimeter of rectangle. Substitute 14 for b and 5 for h.
Additional Example 2: Finding the Perimeter of Rectangles and Parallelograms Find the perimeter of the figure. 16
20 P = 16 + 16 + 20 + 20 = 72 units
Add all side lengths.
Area is the number of square units in a figure. A parallelogram can be cut and the cut piece shifted to form a rectangle with the same base length and height as the original parallelogram. So a parallelogram has the same area as a rectangle with the same base length and height.
Helpful Hint The formula for the area of a rectangle can also be written as A = lw.
Additional Example 3: Using a Graph to Find Area Graph the figure with the given vertices. Then find the area of the figure.
(–1, –2), (2, –2), (2, 3), (–1, 3) Area of a rectangle. A = bh Substitute 3 for b and 5 for h. A=3•5 A = 15 units2
Check It Out: Graph the figure with the given vertices. Then find the area of the figure. (–1, –1), (3, –1), (5, 3), (1, 3) y
(1, 3)
(5, 3)
4
(–1, –1) 4 (3, –1)
x
Area of a parallelogram. A = bh Substitute 4 for b and 4 for h. A=4•4 A = 16 units2
Pg. 395 (1 – 7) All; (10 – 16) All; 19 & 20
Calculators may be used.
Show all work to receive full credit.
