Area and perimeter

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.