Measuring Area

 Area: The number of square units that can be contained on a surface. Imperial area units > Inches in 2 > Feet ft 2 > Yards yd 2

Area can be found by multiplying the length by the width. Area = Length x Width A = l x w *This allows you to find the area inside a square or rectangle

What is the area of this square? Length = 6 in width = 6 in Area = length x width Area = 6 in x 6 in Area = 36 in 2

 Find the length 4.5 ft 2  Find the width 1.5 ft 2 Use the formula for area A = l x w A = 4.5 ft x 1.5 ft A = 6.75 ft 2

Length = 7 yd Width = 4 yd A = l x w A= 7 yd x 4 yd A= 28 yd 2

To find the area of this shape we will need to think of two rectangles. This will let us use A = l x w

 Do the side with the squares first.  The area of L-shaped figures is more difficult.

 A triangle can be though of as half of a square or rectangle. This means the same formula is used but we must half the value.

 You need to make sure you have the base and height correct.

 The base and the height must be perpendicular.

 Find the area of this triangle.

 Sometimes the base is given as two numbers and they must be added together.

 The true height of a triangle is usually inside the figure. In some cases it can be outside the triangle. If this happens it will be marked like this…

 Complete the practice sheet on finding the area of triangles.  I would like you to hand this sheet in when you are finished.  Remember to put the proper area units with the answers.

 Finding the area of a circle requires this formula. This formula has no variations. The radius must be used to solve correctly.  A = πr 2

 If diameter is given we must divide it by two. This will give us the radius for the area formula.

 Find the area of a circle which has a radius of 11.6 cm.

 A circle has a radius of 4.2 m. Find the area of the circle.

 The diameter of a circle was found to be 24.6 in. What is the area of the circle?

 If you did not complete the area of a triangle worksheet you should complete that first and hand it in.  Complete both worksheets on the circle.  The second sheet on circles is being handed in.

 We know how to find the area of squares, rectangles, triangles, and circles.  If a new shape is made out of only these shapes we know, then we can find the area of that shape as well.  The trick is to break the composite shape into shapes you can deal with.

 What is the area of this shape?

 First determine what shapes are contained in the compound shape.  Find the measurements for each part you will need.  Write down the formula for each piece and solve.  Add all the small areas together.

 Many 3D objects contain shapes we can find the area of. This means we can find the total surface area of those objects as well.

 Another very common object we need to be able to find the area of is the cylinder.

 Area of a rectangular Prism SA = 2 ( lw + lh + wh ) Area of a cylinder SA = 2πr 2 + 2πrh

 Find the total surface area of a box with length 5 ft, width 3 ft, and height 2 feet? **(It is a good idea to draw the object)**

 A shipping container has the following dimensions. Height 3.5m, length 12.8m, and a width of 3.0m. A painter needs to know the surface area of the container. Calculate the surface area of the container.

 Complete the worksheet on Surface area of a rectangle prism.

 Cylinders are basically circles with a height component to them.  The thing to be aware of with circles is the formula uses the radius (r).  If you are given the diameter, you must change it to radius before putting it in the formula.

 Don’t forget!!

 An oil barrel is 33.5 in tall. It has a diameter of 22.5 in. Sketch the barrel and calculate the surface area of the barrel. (SA = 2πr 2 + 2πrh)

 A milk holding container is shaped like a cylinder. If the tank is 3.25 m tall and has a radius of 2.5 m, what is the total surface area of the tank? (SA = 2πr 2 + 2πrh)

 A company manufactures aluminum beverage cans in two sizes: Can “A” has a diameter of 2.5in and a height of 4.5in. Can “B” has a diameter of 3in and a height of 3in. Which can requires more aluminum to make? (SA = 2πr 2 + 2πrh) We need to compare the surface area of each can!