### Video Transcript

Work out the volume of a
square-based pyramid with a height of 12 inches and a base length of five
inches.

Let’s begin this question by
sketching a diagram of this pyramid. As we’re told that this pyramid has
a base length of five inches, since this is a square, we know that both the length
and the width will be the same. The height of 12 inches refers to
the perpendicular height of the pyramid. We can recall that the volume of a
pyramid is equal to a third multiplied by the area of the base multiplied by the
height.

So, to find the area of the base,
which is a square in this case, we know that that will be the length multiplied by
the length. So, that’s five times five, giving
us 25 square inches. So, to find the volume of the
pyramid, we take the area of our base, which is 25. So, we have a third times 25 times
the height, which is 12 inches. We can simplify this calculation by
finding a third of 12, which is four. So, we now have the calculation 25
multiplied by four, which is 100. And our units here will be cubic
inches. So, our final answer for the volume
of the pyramid is 100 cubic inches.