Area and Perimeter

What Is Area ? Area is the amount of space inside a shape: Area Area 1cm Area is measured in square units 1cm2 A square centimeter is a square measuring one centimeter in each direction. It can be written as :

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

Example 1 Find the area of the shapes below : (1) 8cm 6cm 4.2m 2.7m (2) (3) 17cm 8cm 12cm 5cm Purple = 48 cm2 Yellow = 11.34 m2 Green = 141 cm2

Area of a Parallelogram and Rhombus Area = Base · Height A = bh A = 60 cm2

The Area Of A Triangle. A = ½ BH Area = ½ x Base x Height Consider the right angled triangle below: 8 cm 5cm What is the area of the triangle ? Area = ½ x 40 = 20cm2 Base Height Of what shape is the triangle half? Rectangle Formula for Area of a Triangle is: What is the area of the rectangle? Area = ½ x Base x Height Area = 8 x 5 = 40 cm2 A = ½ BH

Calculate the area of the triangles below: 10cm 6cm 6.4m 3.2m Red = 30 cm2 Yellow = 10.24 cm2

Calculate the area of the triangle below:

Area of a Trapezoid Area = ½ h ( b1 + b2 ) (b1) (b2)

Calculate the area of the trapezoid below : 16cm 11cm 13cm (11 + 16)(1/2 x 13) = 175.5 cm2

Area = ½ h ( b1 + b2 ) Find the Area of Trapezoid EFGH (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 4in 3.14 x 4in. 12.6in.

When the radius of a circle is given, the following formula should be used. Circumference = 2 r 2 x 3.14 x 5cm 31.4cm 5 cm ∙

Area of a Circle Area = r2 4in 3.14 x 2 x 2 12.56in2

Area of a Circle Area = r2 3.14 x 5 x 5 78.5cm2 5 cm ∙

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 Area changes by c2

John and Mary each have a garden, in the shape of a square 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 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 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 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