The SAT Math sections test three distinct categories of measurement: Perimeter, Area, and Volume. Luckily, many formulas are provided for you at the front of each Math section, but if you do enough practice problems, you’ll soon have these need-to-know formulas committed to memory, and won’t waste valuable test-time flipping pages. Memorizing these formulas is also great practice for the ACT if you plan to take it, since unlike the SAT, the ACT exam does NOT provide them for you!
The perimeter is the distance around any shape. For a triangle, the perimeter will be the sum of the sides. For a rectangle, the formula is P = l + l + w + w, or P = 2l + 2w. For a square, this becomes P = 4s. For other quadrilaterals, you need to know the length of each side in order to find the perimeter, unless you are given more information about the comparative lengths of the sides.
For a circle, the perimeter is equal to the circumference: C = 2πr.
Triangles – To find the area of a triangle, we use the formula A = ½ bh, where b = base and h = height. The base and the height of the triangle must always form a 90 degree angle. Keep in mind that the height can be inside or outside the triangle.
Quadrilaterals – To find the area of any square, use the formula A = s2, where s = side of the square.
To find the area of a rectangle, we use the formula A = lw, where l = length and w = width.
To find the area of a parallelogram, we use the formula A = bh, where b = base and h = height. Remember the base and the height must be perpendicular!
To find the area of a trapezoid, we use the formula A = h(b1 + b2) / 2. Think of it like finding the average of the bases, and multiplying by the height. Just like for parallelograms, the height is perpendicular to the base.
Polygons - To find the area of figures with MORE than four sides, the key is to break up the figure into smaller parts!
Circles – To find the area of a circle, use the formula A = πr2.
The volume of a solid is the amount of space enclosed by that solid. The volume of any solid is always equal to the area of the base multiplied times the height.
The volume of a rectangular solid, therefore, is V = lwh. The volume of a cube (with six equal sides) is V = s3. The volume of a cylinder (a solid whose cross-section is a circle) is found using the formula V = πr2h.
Ready for some more advanced work in measurement? Check out an advanced Volume problem here!
Vivian Kerr is a regular contributor to the Veritas Prep blog, providing advice to help students better prepare for the GMAT and the SAT.