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Understanding Area and Perimeter. Amy Boesen CS255. Perimeter. Perimeter is simply the distance around an object. Everyday applications of perimeter include the distance around a fence or the distance around a pool. To figure out the perimeter of a rectangle, simply add up all the sides.
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Understanding Area and Perimeter Amy Boesen CS255
Perimeter • Perimeter is simply the distance around an object. • Everyday applications of perimeter include the distance around a fence or the distance around a pool. • To figure out the perimeter of a rectangle, simply add up all the sides.
Calculating Perimeter • If the length of this rectangle is 10cm and it has a width of 4cm, what is the perimeter?
Calculating Perimeter cont. • There are two ways to figure this out. The first is to add all four sides. length + length + width + width = perimeter 10 + 10 + 4 + 4 = 28 • The second approach requires you to make an algebraic equation. 2(length) + 2(width) = perimeter 2(10) + 2(4) = 28
Area • Area usually deals with how much space an object covers or how much is needed to cover the object. • Everyday applications of area include how much material it will take to cover a surface.
Units • The units for perimeter and area are not the same. • For example: If we make a dog pen that is 10 feet long and 8 feet wide we would need 36 feet of fencing to surround the pen. However, if we were to calculate the area we would say that the pen covers 80 square feet.
Calculating Area • To calculate the area of a rectangle, simply multiply the length by the width. length x width = area If a rectangle has a width of 6 feet and a length of 8 feet, what is the area?
Calculating Area cont. • To calculate the area of this rectangle, you would have this equation: 6 feet x 8 feet = 48 square feet Since you are multiplying feet x feet, your answer will be square feet. Area is always answered in square units.
Perimeter of Triangles • Finding the perimeter of a triangle is very similar to finding the perimeter of a rectangle. You simply add up the three sides. • If a triangle has one side that is 22 cm long, another that is 17 cm, and a third that is 30 cm long, what is the perimeter? 22cm + 17cm + 30cm = 69cm
Area of Triangles • Finding the area of a triangle is somewhat different than finding the area of a rectangle. • With triangles we no longer can use length times width. We now use base times height. To keep it simple, we will stick to 90 degree triangles for now. • The formula for the area of triangles is: ½ x base x height
Area of Triangles cont. • The height of the triangle is the distance from the base to the point farthest away, measured along a perpendicular line. • The height of this triangle is 4 inches and the base is 6 inches, what is its area?
Area of Triangles cont. • ½ x base x height = area of triangle • ½ x 6 inches x 4 inches = 12 square inches
Distance Around a Circle • The distance around a circle is not called perimeter. It is called the circumference. • To calculate the circumference of a circle we need to use pi. The value for pi is 3.14. Pi is the ratio of the circumference to the diameter of ANY circle.
Circumference • This gives us two possible formulas to calculate the circumference of a circle. One uses radius and the other uses diameter. circumference = pi x diameter or circumference = 2 x pi x radius
Circumference cont. • If the radius of a circle is 5 cm, what is the circumference? circumference = pi x diameter c = 3.14 x 10 c = 31.4cm circumference = 2 x pi x radius c = 2 x 3.14 x 5 c = 31.4
Area of Circles • The formula for the area of circles is a bit more complicated than the others. area = pi x radius squared If a circle has a radius of 8 inches, what is its area? A = 3.14 x 8^2 A = 200.96 square inches
Summary • We have learned many formulas for finding the perimeter and area of various objects such as rectangles, squares, triangles, and circles. • We have learned that perimeter concerns how much is needed to surround an object and that area is how much is needed to cover an object.
Summary cont. • Lastly we learn that the relationship between area and perimeter is somewhat complicated. If you double the area of a square, you do not double its perimeter. However, two objects may have the same perimeters, but different areas or the same area, but different perimeters. • You will understand this relationship more after some additional practice.