# Area and perimeter

Contents

Area and perimeter help us measure the size of 2D shapes. We’ll start with the area and perimeter of rectangles. From there, we’ll tackle trickier shapes, such as triangles and circles.

## Area and perimeter of polygons

Let's now extend our understanding of area to triangles and more interesting quadrilaterals!
Common Core Standard: 6.G.A.1

8:25

Intro to perimeter & area

Great geometry primer on perimeter and area. Listen carefully. Sal explains the concepts so you'll understand them.

Exercise

Find perimeter by counting unit squares

Calculate the perimeter of a shape from its side lengths.

Exercise

Find perimeter when given side lengths

Find perimeter of figures when given an image or context.

Exercise

Transition from unit squares to area formula

Find area of rectangles by multiplying side-lengths.

Exercise

Area & perimeter of rectangles word problems

Find the missing side length of a rectangle when given its perimeter or area. Compare perimeters and areas of rectangles.

10:23

Area of triangle proof

Proving that the area of any triangle is 1/2 b x h

Exercise

Area of triangles

Practice finding the area of right, acute, and obtuse triangles from a diagram.

5:42

Area of parallelogram proof

Guess what's interesting about the opposite sides of a parallelogram? That's right....they are parallel! Let's find the area--base times height

Exercise

Area of parallelograms

Practice finding the area of parallelograms given base and height.

4:48

Area of trapezoids

A trapezoid is a cousin of the parallelogram. However, in trapezoid only two of the opposing sides are parallel to each other. Here's we explain how to find its area.

3:49

Area of kites

Learn how to find the area of a kite. A kite is a type of quadrilateral that is symmetric around one of its diagonals.

Exercise

Area of trapezoids

Practice finding the areas of trapezoids.

3:57

Finding area by rearranging parts

Sometimes it helps to rearrange the parts of geometric figures to find the area. That's what we're going to do here.

5:15

Area of composite shapes

Don't be intimidated by odd looking geometric figures and being asked to find its area. In this example you'll understand that breaking up the figure into smaller geometric shapes that are regular make the task a lot easier.

Exercise

Area challenge

Practice solving problems involving triangles, parallelograms, and composite figures. Exercises include decimals, fractions, and word problems. Area of circles is not included.

Exercise

Areas of shapes on grids

Practice finding the areas of triangles and quadrilaterals on grids.

3:54

Area of a quadrilateral on a grid

Again, some quadrilaterals can be oddly shaped so break it up into shapes where finding the area is more easily determined.

Exercise

Area of composite shapes

Practice finding the areas of complex shapes that are composed of smaller shapes.

## Area and circumference of circles

You already know about area and perimeter of lots of shapes. Now we'll round out those concepts by applying them to circles. Mathematicians call the distance around a circle its circumference and the space inside a circle its area.
In this tutorial, we'll learn that there's another type of pi in the math world, and it's even more awesome than apple pie. We'll use pi to find the circumference and area of any circle in the world, no matter how big or how small!
Common Core Standards: 7.G.B.4

11:05

Radius, diameter, circumference & π

Learn how the number Pi allows us to relate the radius, diameter, and circumference of a circle.

2:01

Labeling parts of a circle

Radius, diameter, center, and circumference--all are parts of a circle. Let's go through each and understand how they are defined.

Exercise

Radius, diameter, & circumference

Practice finding the radius, diameter, or circumference of a circle. For example, if the diameter of a circle is 16, what is its circumference?

4:02

Area of a circle

In this example, we solve for the area of a circle when given the diameter. If you recall, the diameter is the length of a line that runs across the circle and through the center.

Exercise

Area of a circle

1:53

Circumference of a circle

Here we find the circumference, the distance around a circle, given the area. We're building on our knowledge of the parts of circle.

1:31

Area of a shaded region

Here's a fun one: find the area of a shaded region where you first determine the area of a square and then the area of a circle.

3:31

Impact of increasing the radius

If we change the radius of a circle, how does the circumference and area change?

Exercise

Area and circumference of circles challenge

Practice interesting area and circumference problems.

## Scale drawings

Now that you understand lines, you can put lines together to create drawings. A scale drawing depicts an actual object that has been reduced (or enlarged) by a certain amount. The "scale" shows the relationship between those two sizes. After this set of tutorials, you can draw your bedroom "to scale" and practice rearranging your furniture!

4:26

Interpreting a scale drawing

Understand how a scale drawing is converted into real numbers using the scale factor.

5:51

Solving a scale drawing word problem

See how we solve a word problem by using a scale drawing and finding the scale factor.

Exercise

Interpreting scale drawings

3:18

Making a scale drawing

An urban planner needs your help in creating a scale drawing. Let's use our knowledge about scale factor, length, and area to assist.

Exercise

Constructing scale drawings

An urban planner needs your help in creating a scale drawing. Let's use our knowledge about scale factor, length, and area to assist.