Perimeter Perimeter is the total mesurement of all of the lines that make up the shape. Perimeter is very useful in the real world, just like area. Let's say you were building a fence to go all the way around your property. If you mesure the length and width of your yard, then you can find the perimeter and figure out how much lumber to buy. "Shaping" It All Up AREA Area is all of the space inside of any enclosed figure, like circles and rectangles. Area is used many times in the real world. If you were painting a wall, and one gallon covered a 6ft x 6ft portion of that wall, then how many gallons would you need? Well, all you would need to do is find the area of the wall! Perimeter Perimeter is the total measurement of the outside of an enclosed figure. Perimeter, just like area, is used in day-to-day life. Let's say you were building a fence around your yard. Well, all you have to do is measure the length and width of your yard to find out how much lumber you need! There are different shapes that are needed by perimeter, and they each have their own formula. When finding the perimeter of a rectangle, you add two times the length and two times the width, but with a circle, you multiply the radius times pi. * In a circle, the perimeter is called the circumference. Pi Pi is the ratio of the circumference of a circle to the diameter of a circle. That just means that everytime you divide the circumference of the circle by the diameter, no matter what circle it is, the answer will be pi. Pi is an irrational number, which means that it has no end, though it is often expressed as 3.14. *Because pi is such a large number, it is often expressed using this symbol. Now that you know everything, let's shape it up! The Shapes The Circle The Parallelogram The Square The Composite Figure The Triangle The Rectangle The Trapezoid The circle is a very common shape. Circles make the bases of cans, lids to drinks, and lenses on cameras to name a few. We see many circles in daily life. To figure out the circumference of a circle, you multiply its diameter times pi or two times the radius times pi. Example: If a circle has a radius of 4 meters, what is the circumference of the circle? C = 2 x 3.14 x 4 C = 25.12 meters To find the area of a circle,

you multiply pi times the radius

squared. If the radius of a circle is 25

centimeters,

what is the area of the circle? Imagine you have a trampoline in your backyard,and you want to put a net around it. If the edge to the middle point of the trampoline is 8 feet, how much netting will you need? To find the area of a triangle, you multiply one half times the base of the triangle times the height of the triangle. If a triangle has a base of 13 inches, and a height of 7 inches, what is the area of the triangle? a = 1/2 x 13 x 7 a = 45.5 square inches If the height of a triangle is seventeen meters, and the width of it's base is twenty-four meters, what's the area of the triangle? a = 1/2 x 17m x 24m a = 204 square meters Triangles are used for many different things. Much of today's architecture is made up of triangles, such as the Eiffel Tower and pyramids. Many roofs are made up of triangles as well. When finding the perimeter of a triangle, you add up the length of all sides. Find the perimeter. P= 24in + 29in + 13in P= 66in Let's say you need to string lights on the triangular part of your roof, and one side is 12ft, another is 15ft, and the last is 6ft. How many feet of lights do you need? A company's logo is in the shape of a triangle. They need to know how much area it will take up if they have a 50 square feet board to place it on. If the triangle has a base of 8 feet and a height of 5 feet, what is it's area? A = 1/2 x 8 x 5 A = 2.5 x 8 A = 20 square feet A = 3.14 x 25 x 25 A = 1962.5

square centimeters Jill wants to find how much

area will need to be covered

on her clock. If the minute hand

is the radius that extends 8 inches,

how much area will be covered

on her clock? A = 3.14 x 8 x 8 A = 200.96 inches The area covered on Jill's

lock will be 200.96

square inches. C= 2(3.14)(8) C= (6.28)8 C= 50.24 feet To find the area of a parallelogram, you must multiply the the base times the height. If a parallelogram has a base of 9 centimeters and a height of 18 centimeters, what's its area? A= 9 x 18 A= 162 square cm Mitche is building a lemonade stand sign in the shape of a parallelogram and wants to paint it purple. How much area will she need to paint if it has a height of 14 inches and a base of 15 inches? A= 14 x 15 A= 210 inches P= 12 + 15 + 6 P= 33 feet To find the perimeter of a paralellogram, you double the length and width and add them. Find the perimeter. P= (10) 2 + (6) 2 P= 20 + 12 P= 32 feet After Mitche painted her sign, she decided to border it in lace. How much lace will she need if its length is 20 inches and its width is 13 inches? P= 2(20) + 2(13) P= 40 + 26 P= 66 inches To find the area of a composite figure, you have to break down the figure and find the area accordingly. Find the area. A= 1/2 x bh

A= 1/2 x 2 x 5

A= 1 x 5

A= 5 square meters 1- 2- 3- A= lw

A= 9 x 3

A= 27 square meters A= lw

A= 6 x 2

A= 12 square meters A= 12+27+5

A= 44 square meters Mary Kate's wall looks like the figure below. If she wants to paint the wall. What is its area? Trapezoid: Area of a Trapezoid= 1/2h (b + b)

A= 1/2(3)(7+6)

A= 1/2(3)(13)

A= 1.5(13)

A= 19.5 feet squared 1 2 Rectangle: A= l x w

A= 7 x 2

A= 14 square feet A= 19.5 + 14

A= 33.5 square feet To find the perimeter of a composite figure, you add up the length of all the sides. To find the perimeter of a square, you add up the lengths of every side. What is the perimeter of a square if all of its sides measure 12 units? A = 12+12+12+12 A=48 sq. units Jim is making a brick wall to go around his square yard. If one side measures 16 meters, how many meters of brick will surround his yard? A = 16+16+16+16 A = 64 meters

Jim will have 64 meters of brick around his yard. To find the area of a square, you multiply the length times the width. What is the area of a square if its length and width measure

6 mm? A = l x w A = 6 x 6 A = 36 mm Choca is making a rug that will be in the shape of a square. If all of its measures are 12 ft, how much area will she fill in with carpet to complete her rug? A = l x w A = 12 x 12 A = 144 square feet

Choca will fill her rug up

with 144 square feet of carpet. 2 To find the area of a trapezoid, you multiply one half times the height of the trapezoid times the length of both bases added together. A = 1/2 x h (b + b ) What is the area of a trapezoid if its height is 6 in with one base at 2 in and another base at 5 in? 1 2 A = 1/2 x 6(2+5) A = 3(7) A = 21 in 2 Anna's mirror is in the shape of a trapezoid, and she wants to cover it so it will have a blue tint. How much area of tint cover will she use if its height is 8 in and its top is 9 in with a bottom of 18 in? A = 1/2 x h (b + b ) 1 2 A = 1/2 x 8(9+18) A = 4(27) A = 108 in

Anna will use 108 in of tint paper on her mirror. 2 2 To find the perimeter of a trapezoid, you add up all the lengths of every side of the trapezoid. What is the perimeter

of a trapezoid with sides

measuring: 10, 2, 18, and

6 inches? Laura wants to frame her mirror. If its side measures are 20 in, 24 in, 6 in, and 6 in, how much frame material will she need to go around her trapezoid? P = 20+24+6+6 P = 56 in

Laura need 56 in of framing material to go around her trapezoid mirror. P = 10+2+18+6 P = 36 in To find the area of a rectangle, you multiply its length and width. What is a rectangle's area if it is 7 mm long and 9 mm wide? A = l x w A = 7 x 9 A = 63 mm 2 Bobby is planning to build a rectangular garden, and he needs to plow it so he can plant cucumbers. How many meters will he plow if it has a length of 16 m and a width of 18 m? A = l x w A = 16 x 18 A = 288 m

Bobby will plow 288 m. 2 To find the perimeter of a rectangle, you add up the lengths of all the sides. What is the perimeter of a rectangle with a length of 21 units and a width of 6 units? P = 21+6+21+6 P = 54 units Dalton wants to build a fence around his rectangular garden. If it is 24 m long and 16 m wide, how much fence will Dalton need to surround his garden? P = 24+16+24+16 P = 80 m

Dalton needs 80 meters of fence

to surround his garden. Composite figures are just combinations of different shapes. We see them a lot in everyday life, like on the screen you're viewing this Prezi on right now. They also make envelopes and arrows. Rectangles are used very frequently

in our daily lives. They make up picture

frames, doors, and boxes. Parallelograms are actually used

a lot in our lives as well. Seeing

as squares and rectangles are also

parallelograms, they make up

speakers, computer screens, etc. 3 feet 2 feet 2 feet 7 feet Find the perimeter of this figure. P = 2 + 2 + 6 + 3 + 2 + 7 P = 22 feet 6 meters P = 9 + 3 + 6 + 2 +2 + 2 + 2 + 6 P = 28 meters Find the perimeter of this figure. Squares are probably the

most commonly found shape

in the world. It's used for multiple

things, such as: CD cases, Cheez-Its,

and Rubik's Cubes. Trapezoids are used a lot in everyday life. We see them in lamp shades, windows, and the inlays of many doors.

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# "Shaping" It All Up

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