Name: _____________________________________________ Period



Name: _____________________________________________ Period: ______

Packet 5: Perimeter and Area

Perimeter

The perimeter of a polygon is the sum of the lengths of the sides of the polygon. Think of a police show when they “have the perimeter surrounded”.

Perimeter means add up all the sides.

For a circle, we call the perimeter “circumference”.

Perimeters and Lengths are measured in feet, inches, meters, etc.

Area

The Area of a figure is the number of square units needed to cover a surface.

Think of an area rug.

Areas are measured in square feet, square inches, square meters, etc.

| | |AREA Formula |CIRCUMFERENCE (Perimeter) Formula |

|Circle | | |C = [pic]d or C = 2[pic]r |

| | |A = [pic]r[pic] | |

|POLYGON | |AREA Formula 1 |AREA Formula 2 |

|Square | | |A = ½ d[pic] |

| | |A = s[pic] | |

|Rhombus | | |A = ½ d[pic]d[pic] |

| | |A = bh | |

|Parallelogram | | |

| | |A = bh |

|Rectangle | | |

| | |A = lw or |

| | |A = bh |

|Triangle | | |

| | |A = ½ bh |

|Trapezoid | | |

| | |A = ½ h( b [pic]+ b[pic]) |

| | | |

Find the perimeter of the following figures.

|1. |2. |

|3. |4. |

|5. |6. |

|7. |8. |

Find the exact value for area of each of the following figures. Make sure that you start by writing down the formula and then show ALL of your work!!!

1. A = ______ 2. A = ______

3. A = ______ 4. A = ______

5. A = ______ 6. A = ______

7. A = ______

Area of Shaded Figures

Sometimes you need to find the area of an odd-shaped figure. We can use our knowledge of area of polygons and circles to help us find the area of an odd-shaped figure.

[pic]

Distance Formula

Distance: in the coordinate plane given points (x1, y1) and (x2, y2)

Distance Formula [pic]

|1.   |2.   |

|(-2, 4) and (3, 4) |(-3, 9) and (-3, 13) |

| | |

| | |

|3.   |4.   |

|(3, 2) and (0, 2) |(8, -3) and (8, -4) |

| | |

| | |

|5.   |6.   |

|(-7, -1) and (-11, -1) |(-1, -1) and (-1, -2) |

| | |

| | |

|7.   |8.   |

|(8, -3) and (13, -3) |(13.3, 2.7) and (1.8, -1.8) |

| | |

| | |

|9.   |10.   |

|(-4, 8) and (-4, 11) |(-6, 6) and (-6, 10) |

| | |

| | |

|11.   |12.   |

|(21, 2) and (18, 16) |(-9.1, -6.3) and (-10.8, -20.6) |

| | |

| | |

|13.   |14.   |

|(11, -3.9) and (17.2, -0.2) |(23, 19) and (21, 31) |

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| | |

|15.   |16.   |

|(2, 8) and (0, 8) |(4.3, -22.7) and (10.5, -35.9) |

| | |

| | |

|17.   |18.   |

|(-17.5, 11.7) and (-32.2, 2.3) |(2.8, 3.3) and (-7.4, 1) |

| | |

| | |

Use the Distance Formula to find the lengths of sides in order to find the area of the figure.

|1.   |2.   |

|Find the area of the square whose vertices are |Find the area of the trapezoid whose vertices are |

|(4, 7), (1, 7), (1, 3), and (4, 3) |(-6, 3), (5, 0), (5, 3), and (0, 0) |

| | |

| | |

|3.   |4.   |

|Find the area of the triangle whose vertices are |Find the area of the quadrilateral whose vertices are |

|(-9, 8), (-9, 16), and (-17, 8) |(1, 4), (-5, 0), (7, -3), and (-1, -8) |

| | |

| | |

|5.   |6.   |

|Find the area of the trapezoid whose vertices are |Find the area of the triangle whose vertices are |

|(-7, -4), (-7, 1), (0, -4), and (-4, 1) |(6, 4), (3, 4), and (6, 1) |

| | |

| | |

|7.   |8.   |

|Find the area of the parallelogram whose vertices are |Find the area of the quadrilateral whose vertices are |

|(0, -1), (0, -4), (5, -1), and (5, -4) |(-3, -10), (-5, -1), (2, -1), and (-1, 3) |

| | |

| | |

|9.   |10.   |

|Find the area of the triangle whose vertices are |Find the area of the trapezoid whose vertices are |

|(-7, 1), (1, -7), and (-7, -7) |(8, -4), (3, -8), (16, -8), and (3, -4) |

| | |

| | |

|11.   |12.   |

|Find the area of the square whose vertices are |Find the area of the quadrilateral whose vertices are |

|(-1, -5), (-8, -5), (-1, -2), and (-8, -2) |(-5, -10), (-2, 3), (-8, -1), and (2, -3) |

| | |

| | |

|13.   |14.   |

|Find the area of the trapezoid whose vertices are |Find the area of the parallelogram whose vertices are |

|(8, 5), (1, 5), (16, 9), and (1, 9) |(-5, 11), (-8, 11), (-8, -1), and (-5, -1) |

| | |

| | |

|15.   |16.   |

|Find the area of the triangle whose vertices are |Find the area of the quadrilateral whose vertices are |

|(-2, 4), (1, 8), and (-2, 8) |(-6, -2), (-4, -11), (2, -3), and (-1, 2) |

| | |

| | |

|17.   |18.   |

|Find the area of the trapezoid whose vertices are |Find the area of the quadrilateral whose vertices are |

|(2, 0), (2, 7), (-14, 0), and (-6, 7) |(-5, -2), (-7, 5), (0, 1), and (-3, 8) |

| | |

| | |

Find the Side Given Perimeter or Area

When working with problems involving formulas follow these steps:

1. Select the appropriate formula.

2. Plug in given information.

3. Solve for unknown.

4. Label answer.

5. Look back.

|1. If the area is 141.9 m2, what is the height? |2. The area of a circle is 78.5 sq. cm. What is the radius of the |

| |circle? (Use 3.14 for π). |

|3. The circumference of a circle is 208π. Find the diameter. |4. The perimeter of a rectangle is 165 ft. The height of the |

| |rectangle is 39 ft. Find the length of the base of the rectangle. |

|5. The perimeter of the following figure is 40 ft. Find the value of|6. The area of the following figure is 60 ft2. Find the value of x. |

|x. | |

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Find the area and perimeter of the following triangles. (Remember for right triangles to use a2 + b2 = c2)

|1. |2. |

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Word Problems

|1. The spray from a spinning lawn sprinkler makes a circle with a 40’ |2. Gears on a bicycle are just circles in shape. One gear has a diameter|

|radius, what is the circumference and area of the circle? |of 4”, and a smaller one has a diameter of 2”. |

| |How much bigger is the circumference of the larger one compared to the |

| |smaller one? |

|3. If a triangular sail has a vertical height of 83 ft and horizontal |4. If the area of a small pizza is 78.5 in2, what size pizza box would |

|length of 40 ft, what is the area of the sail? |best fit the small pizza? (Note: Pizza boxes are measured according to |

| |the length of one side.) |

|5. A rectangular field is to be fenced in completely. The width is 28 yd|6. Grace is making a display board for the school talent show. The |

|and the total area is 1,960 yd2. What is the length of the field? |display board is a 6 ft by 11 ft rectangle. She needs to add a ribbon |

| |border around the entire display board. What is the length of ribbon |

| |that she needs? |

|7. The perimeter of a rectangular field is 40 ft and its width is 10 ft.|8. Tammy needs to rent an office building. He needs 10,000 square feet |

|Find the area of this field. |of space. If |

| |Tammy found a building to rent that is 81 feet by 102 feet, is this |

| |building large |

| |enough to meet Tammy’s building needs? |

|9. Sara wants to buy wood to make a frame for her picture. Her picture |10. A certain wall is 13’ by 9’. A can of paint will cover 50 square |

|is a 12” by 10” rectangle. What is the total length of the wood strips |feet. Will it be enough? |

|she will need for her project? |Explain. |

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Perimeter is only the outside!

Area covers the inside!

5

3

10

3

8

6

6

8

10

4

20

4

4

x

12

8

6

6

12

15

x + 3

5

x + 8

x

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