Area

Area

Area is the amount of 2D space a shape takes up. Shapes can be simple, like rectangles or triangles, or it can be made up of different shapes. Area can also cover the outside of 3D objects. Think about area like carpet. It can cover a floor in all different shapes. It can also cover shapes. Once I saw a car covered in carpet; it wasn't a good look.

Area (copy into books)

• Area is the amount of 2D space a shape takes up.

• Area is measured in how many squares of cm or metres that could fit in the 2D space.

• If you could fit eight 1cm x 1cm squares in a rectangle, then the rectangle is 8cm².

Area of a rectangle (copy)

• The area of a rectangle is the length multiplied by the width.

• A = L x W

• The units need to be the same.

  For example, if you had a room 3m by 4m, the carpet inside would need to be 12m².

Multiple Choice

What is the area of a rectangle 7m by 3m?

• 21m²

• 9m²

• 10m²

• 24m²

• 21

Make sure you write the units with no spaces!

Fill in the Blanks

Fill in the Blanks

Area of a Triangle

The area of a triangle is half the area of a rectangle drawn around the outside.

Perpendicular Height

The perpendicular height is also known as the "right angle height". It is at a right angle to the base of the triangle.

Area of Triangle (copy down)

•  $A\ =\frac{1}{2}bh$  

• Where: A = Area
  

•               b = base length
  

•               h = perpendicular (right angle) height
  

Multiple Choice

Find the area of the triangle.

• 30 m²

• 60 m²

• 16 m

• 30 m

Multiple Choice

Find the area of the triangle.

• 10 cm²

• 24 cm²

• 12 cm²

Multiple Choice

Find the area of the triangle

• 31.5 units²

• 63 units²

• 77 units²

• 38.5 units²

Multiple Choice

Find the area of this triangle.

• 20 cm²
• 35 cm²
• 40 cm²
• 17.5 cm²

Multiple Choice

A triangle has an area of 117 cm². If the base is 26 cm, what is the height?

• 36 cm
• 18 cm
• 9 cm
• 4.5 cm

Area of a Circle

The area of a circle is:  $A_{circle_{ }}=\pi r^2$ 

You don't need to understand how this formula is found, but here are some fun videos showing you how it works.

Area of a circle using rectangles

The last video showed you how we found the area of a circle using triangles. Here's how we found it using rectangles.
First, cut up a circle into even pieces, and try to make it fit into a rectangle.

Area of a circle using rectangles

That shape wasn't a very good rectangle. What if we cut it into smaller pieces?

Area of a circle

If we managed to cut the circle into super small pieces, it starts to look like a rectangle.

The height is the same as the radius, r. The length around the outside of the circle is the circumference 2πr. So the length of the rectangle is half of that:πr. Therefore:

A = length x width.

A = r x πr

A = πr²

Copy down the next slide

Yes all of it.

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

If you are given the diameter, how can you calculate the radius?

• Multiply the diameter by 2

• Subtract 2 from the diameter

• Add 2 to the diameter

• Divide the diameter by 2

Multiple Choice

What is the radius of this circle?

• 18

• 10

• 9

• 8

Multiple Choice

What number can you use to approximate pi?

• 1.41

• 2.00

• 3.14

• 5.14

Multiple Choice

find the area of the circle with radius 3 cm below.

• 100 cm²
• 225 cm²
• 9 cm²
• 28.26 cm²

Multiple Choice

Find the area of the circle, giving your answer to 1 decimal place.

• 113.1cm²

• 28.3cm²

• 6.3cm²

• 37.7cm²

Multiple Choice

Find the area of the circle, giving your answer to 1 decimal place.

• 201.1cm²

• 201.0cm²

• 804.2cm²

• 804.2m²

Multiple Choice

In terms of area and space, a _____ is half of a circle.

• circumference

• pi

• semicircle

• composite figure

Multiple Choice

what is the area of this semicircle ?
d = 8 cm 

• 100.48 cm²
• 80 cm²
• 200.96 cm²
• 25.12 cm²

Composite Shapes

Some shapes can be made up of the area of other shapes. You can add areas together, or take areas away. Think of the car with carpet all over it. The area of carpet on the roof may be a rectangle. Then you could add another larger rectangle on the sides of the car. Then you might subtract area for the windows.

Multiple Choice

What is the area of the shaded region?

• 20 sq cm

• 4 sq cm

• 30 sq cm

• 24 sq cm

Multiple Choice

Find the area of the shaded region: 

• 350 cm²
• 137.5 cm²
• 212.5 cm²
• 484.2 cm²

Multiple Choice

What is the area of the shaded figure?

• 296.96 m²

• 248.96 m²

• 98.24 m²

• 73.13 m²

Multiple Choice

Which of the following is closest to the area of the figure shown?

• 420 cm²

• 521 cm²

• 320 cm²

• 484 cm²

Multiple Choice

A local restaurant places tissue-paper liners in baskets for yeast rolls like the liner pictured.

About how many square centimeters of tissue paper are needed to make one liner?

• 200.96 cm²

• 379.3 cm²

• 251.2 cm²

• 253.6 cm²