SAT Subject Test Mathematics Level 2

THE TEST MAKERS’ FAVORITE SOLID

The test makers’ favorite solid is the rectangular solid. That’s the official geometric term for a box,
which has 6 rectangular faces and 12 edges that meet at right angles at 8 vertices.

The surface area of a rectangular solid is simply the sum of the areas of the faces. That’s what the
formula “Surface Area = 2ℓw + 2wh + 2ℓh” says. If the length is ℓ, the width is w, and the height is h,
then two rectangular faces have area ℓw, two have area wh, and two have area ℓh. The total surface
area is the sum of those three pairs of areas.

SURFACE AREA OF A RECTANGULAR SOLID

If  the length  is  ℓ,  the width   is  w,  and the height  is  h,

the formula is:

Surface Area    =   2ℓw +   2wh +   2ℓh

Instead of the surface area, you may be asked to find the distance between opposite vertices of a
rectangular solid. Look at Example 2.

Example 2