ShmoopTube

00:03

Here’s your shmoop du jour…

00:05

Two vertices, W and Z, of the square shown

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below have the coordinates (0, 3) and (4, 0), respectively. 

00:12

What is the area of the square?

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And here are the potential answers...

00:18

Ooh, totally cool and clever problem that really tests our ability to visualize, slice, and dice.

00:24

Let’s first plot the coordinates we’re given to try to visualize this square.

00:28

(0, 3) for point W…so we start at the origin, and move up 3 units.

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(4, 0) for point Z… so we can just move to the right 4 units.

00:37

Since both of these points are vertices of the square, we can just connect the two to get one side of a square.

00:43

Okay wait… what’s the distance between points W and Z?

00:48

Calling Pythagoras…1-800-Pythagoras…Come in...

00:52

We can see use the Pythagorean theorem to find the length between W and Z…

00:55

“a squared plus b squared equals c squared.”

00:59

And that gets us 3 squared plus 4 squared is c squared which is 9 plus 16, or 25.

01:06

Take the square root to get 5 equals the line between W and Z.

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This is a SQUARE…which means that all sides are equal. All of them are 5.

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And the formula for the area of a square is just base times height – so if we know one

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side we know everything, more or less… And that gets us 5 times 5 which is... 25.

01:27

Answer… C. As in… “Careful – it’s hot.”

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