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A#121 NAME DATE PER. AREA & PERIMETER OF RECTANGLES, PARALLELOGRAMS, and TRIANGLES Find the perimeter and area of each rectangle. 7 in 1. P 3.2 in A 2. P 8 A 45 Find the indicated measures. 3. P The

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Hi, welcome to Math Antics. In our last geometry video, we learned that all 2-dimensional shapes have a 1-dimensional quantity called Perimeter which is basically the outline of the shape. In this video, we're going to learn that these shapes also have a 2-dimensional quantity called Area. To help you understand what Area is, let's start by imagining a line that's 1 cm long. Now, let's imagine moving that line in a perpendicular direction a distance of 1 cm. But while we move it, it leaves a trail… almost like the end of a paint brush. By moving the 1-dimensional line that way, we formed a 2-dimensional shape, and all the space (or surface) that we covered along the way is the Area of that shape. …which as you can see here is just a square. Ok, but how much area does this square have? Well, our original line was 1 cm long, and we moved it a distance of 1 cm, so we could say that this shape is a square centimeter. Just like a centimeter is a basic unit for measuring length, a square centimeter is a basic unit for measurement for area. But there are other units for area too. For example, instead of a centimeter, what if our line had been a meter long, and then we moved it 1 meter? The area we'd have gotten would be 1 square meter! Or, what if it was a mile long, and we moved it a mile!? We'd have a square mile of area. So, just like with perimeter, the units of measurement are very important when we're talking about area! Alright, so that gives you a good idea of what area is, but how do we calculate area mathematically? Well, there's some special math formulas (or equations) that we can use to find the area of different shapes. In this video, we're going to learn the formula for squares and rectangles and the formula for triangles. To find the area of any square or rectangle, all we have to do is multiply its two side dimensions together. They're usually called the length and the width, so the formula looks like this: Area equals length times width. But it's often written with just the first letters of each word as abbreviations: ‘A’ for Area, ‘L’ for Length and ‘W’ for Width. So let's see if that formula works for our original square centimeter. If we multiply the length (1 cm) times the width (1 cm×, what do we get? Well, 1 × 1 is just 1, but what about cm x cm? Cm x cm just gives us square centimeters, which we can write like this using a '2' as an exponent. We read this as quot;centimeters squared” and it's just a shorter way of writing cm x cm. So whenever you see units like centimeters squared, or inches squared, or meters squared, or miles squared, you know it's a measurement of the 2-dimensional quantity area. Ok, our formula (area equals length times width) worked for our square. Now let's see if it works for a rectangle. Here's a rectangle that's 4 cm wide and 2 cm long (or tall) First, we plug the length and width into our formula (2 cm and 4 cm) Then we just multiply… 2 × 4 equals 8 and cm x cm is cm squared. So, according to our...

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