(lively music) - Good morning, my magnificent mathematicians.

I'm so excited to be with you this morning.

We are about to have so much fun today learning more about math and growing our brains.

Can you help me out with the surprise project I'm working on?

It's actually a surprise for Frisbee.

Shh!

He loves to go to the park and run around in the grass, but here at home, he doesn't have anything like that.

The first problem is that the yard doesn't have a fence.

So I need to figure out the perimeter of the yard to know how much the fence will cost.

The second problem is that our backyard has a lot of trees so it doesn't get much sun or have any good grass.

But I've done my research, and I found out that you can buy grass.

They sell Soft Bermuda at our local outdoor store.

It costs $1.44 for one square foot of grass.

Now, they don't sell it in actual squares, they sell it on big rolls.

But once I know how many square feet of grass I'll need for the whole yard, I can figure out how many rolls to buy.

Okay.

Here is a map of the backyard.

(objects crashing) Did you all hear something?

Well, you can see where the trees are and then where I want to put the grass.

And this would be so much easier without the trees because we would have one big rectangle.

But my plan is to divide this into smaller rectangles and calculate the area of each one.

Then we'll add all those areas together.

Okay.

First problem.

I need to put a fence around the perimeter of the yard.

So if we walked around the yard, we would walk 18 feet, and 20 feet, and 18 feet, and 20 feet again.

Our formula for perimeter is 2 X length + 2 X width.

Okay, let's plug in our numbers and solve this problem.

Perimeter equals 2 X 20 + 2 X 18.

That gives us 40 + 36 for a total of 76 feet.

So I'll tell the fence company that I need 76 feet of fence installed.

Alright, now let's figure out how much grass we need.

Remember perimeter is the distance around a shape.

The area is that space inside.

And I need the grass to cover the space inside and all around the trees.

I certainly don't just want grass around the perimeter of the yard.

That would look really, really funny, right?

To find the area inside, I'm going to section the yard off into smaller rectangles and we'll find the area of each one.

Let's make this left part between the trees our first rectangle.

Then we'll do this big middle section.

Then we'll section off this right part.

And then we'll have one little rectangle left.

Right here.

Okay.

So in all, we've got four rectangles to find.

And to find the area of each one, we'll use the formula: area = length X width.

And remember area covers the space inside the shape.

So your answer will always be in square units.

Now, for this problem we're measuring in feet, which means our answer will be in square feet.

Let's start with the left rectangle.

The length is 10, and the width is 4.

If we plug those numbers into our formula, we get area = 10 X 4, that's 40 square feet.

The second rectangle covers this big area in the middle.

The length is 18 feet, and the width is 9 feet.

If we plug those measurements into our formula, we get area = 18 X 9.

That's 162 square feet.

The third rectangle covers the area on the right side.

The length is 12 feet, and the width is 7 feet.

If we plug those numbers in, we get area = 12 X 7 for 84 square feet.

We still have one little rectangle.

Right down here.

The width is 2 feet and the length is 4 feet.

Area = 2 X 4, that's 8 square feet.

Now we need to add all those parts together to get the whole.

40 + 162 + 84 + 8 = 294.

So I need 294 square feet of grass.

Wow.

That's a lot.

Let's see how much that will cost.

294 square feet, and it costs $1.44 per square foot.

So let's multiply.

294 X $1.44 = $423.36.

That's a lot.

Would you pay that much for grass?

Woo, I sure hope Frisbee loves his surprise.

- Oh, here's Ms. Post.

- Frisbee, we've been talking about you.

- I have been eavesdropping.

I heard everything.

It sounds amazing.

You are so thoughtful, Ms. Post.

- Well, thank you for your help today while I figured out this project.

That was some really useful math that helped us solve a real problem.

I hope you have an amazing day, and I'll see you next time on Rise and Shine.

- Bye.

- Bye-bye.