Area and Perimeter What Is Area Area is

Area and Perimeter

What Is Area ? Area is the amount of space inside a shape: Area Area Area Area Area Area is measured in square units 1 cm 2 A square centimeter is a square measuring one centimeter in each direction. 1 cm It can be written as : 1 cm 2 1 cm

Area of a Rectangle and Square Area = Length · Width A = bh

Example 1 Find the area of the shapes below : (1) 6 cm (2) 2. 7 m 8 cm 4. 2 m 17 cm (3) 5 cm 12 cm 8 cm Purple = 48 cm 2 Yellow = 11. 34 m 2 Green = 141 cm 2

Area of a Parallelogram and Rhombus Area = Base · Height A = bh A = 60 cm 2

The Area Of A Triangle. Consider the right angled triangle below: What is the area of the triangle ? Area = ½ x 40 = 20 cm 2 5 cm Height 8 cm Of what shape is the triangle half? Rectangle What is the area of the rectangle? Area = 8 x 5 = 40 cm 2 Base Formula for Area of a Triangle is: Area = ½ x Base x Height A = ½ BH

Calculate the area of the triangles below: 6 cm 10 cm 3. 2 m 6. 4 m Red = 30 cm 2 Yellow = 10. 24 cm 2

Calculate the area of the triangle below: Area = 6

Area of a Trapezoid Area = ½ h ( b 1 + b 2 ) (b 1) (b 2)

Calculate the area of the trapezoid below : 11 cm 13 cm 16 cm (11 + 16)(1/2 x 13) = 175. 5 cm 2

Find the Area of Trapezoid EFGH Area = ½ h ( b 1 + b 2 ) (4+6)(1/2 x 4) = 20

RADIUS The radius is the distance from the center of a circle to any point on a circle.

DIAMETERS

We use Pi as the measurement to help us find the circumference and area of a circle. Pi, not Pie!

HINT: Pi =3. 14

Two formulas are used in finding the circumference of a circle. Circumference = d 3. 14 x 4 in. 12. 6 in. 4 in

When the radius of a circle is given, the following formula should be used. Circumference = 2 r 2 x 3. 14 x 5 cm ∙ 5 cm 31. 4 cm

Area of a Circle Area = r 2 4 in 3. 14 x 2 12. 56 in 2

Area of a Circle Area = r 2 3. 14 x 5 ∙ 5 cm 78. 5 cm 2

Change in Dimension Polygons If you change dimensions by a and b then Area changes a x b

Change in Dimensions Circles If you change the radius by c then 2 Area changes by c

• John and Mary each have a garden, in the shape of a square. If the area of John’s garden is four times the area of Mary’s garden, how do the perimeters of the two gardens compare? • The perimeter of Johns garden is twice the perimeter of Mary’s garden. Width and Length are both doubled.

• Jenni made a small table for a class project. The top of the table is triangular. Her mother wants her to make a larger table. If she changes the dimensions so that both the base and the height of the triangle are tripled, how will the area of the tabletop change? • The area will be 9 times larger.

• Paula and Munos each made a rectangular garden. Paula’s garden is half the length of Munos’. How do the areas of the gardens compare if the gardens have the same width? • The area of Paula’s garden is half the area of Munos’ garden OR The area of Munos’ garden is twice the area of Paula’s garden.

• Martha made a circular quilt with a radius that is double that of the pattern. How does the area of her quilt compare to that of the pattern? • The area of the quilt is 4 times the area of the pattern. (22 is 4)

• Jack has his dog secured at a stake with a 5 foot chain. If he wants to give his dog nine times the area that he currently has, what length chain should he use? • Jack will need to multiply the chain length (radius) by 3 to multiply the area by 9 (32)

• A rectangular bathroom has dimensions of 4 ¾ ft by 4 ½ ft. The floor is made of tiles with side length of 1 foot. What is the number of tiles that will cover the bathroom floor? You will need 21. 375 tiles.

• The area of a square is 144. What are the length of the sides? • 12 • The circumference of a circle is 36 inches. What is the radius? • 36 ÷ 3. 14 = 11. 465 = diameter • 11. 465 ÷ 2 = 5. 7325 = radius