# SAT – Maths : Formula Sheet

Area of a Circle

\begin{aligned} & A=\pi r^2 \\ & C=2 \pi r \end{aligned}
$A=\pi r^2$
$$\pi$$ is a constant that can, for the purposes of the SAT, be written as 3.14 (or 3.14159 )
$$r$$ is the radius of the circle (any line drawn from the center point straight to the edge of the circle)

Circumference of a Circle

$C=2 \pi r(\text { or } C=\pi d)$

$$d$$ is the diameter of the circle. It is a line that bisects the circle through the midpoint and touches two ends of the circle on opposite sides. It is twice the radius.

Area of a Rectangle

$$A=l w$$
$$l$$ is the length of the rectangle
$$w$$ is the width of the rectangle

Area of a Triangle

\begin{aligned} A & =\frac{1}{2} b h \\ \end{aligned}

$$b$$ is the length of the base of triangle (the edge of one side)
$$h$$ is the height of the triangle
In a right triangle, the height is the same as a side of the 90-degree angle. For non-right triangles, the height will drop down through the interior of the triangle, as shown above (unless otherwise given).

The Pythagorean Theorem

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$a^2+b^2=c^2$

In a right triangle, the two smaller sides ( $$a$$ and $$b$$ ) are each squared. Their sum is the equal to the square of the hypotenuse (c, longest side of the triangle).

Properties of Special Right Triangle: Isosceles Triangle

An isosceles triangle has two sides that are equal in length and two equal angles opposite those sides.
An isosceles right triangle always has a 90-degree angle and two 45 degree angles.
The side lengths are determined by the formula: $$x, x, x \sqrt{2}$$, with the hypotenuse (side opposite 90 degrees) having a length of one of the smaller sides * $$\sqrt{2}$$.
E.g., An isosceles right triangle may have side lengths of 12,12 , and $$12 \sqrt{2}$$.

Properties of Special Right Triangle: 30, 60, 90 Degree Triangle

•  A 30, 60, 90 triangle describes the degree measures of the triangle’s three angles.
• The side lengths are determined by the formula: $$x, x \sqrt{3}$$, and $$2 x$$
• The side opposite 30 degrees is the smallest, with a measurement of $$x$$.
• The side opposite 60 degrees is the middle length, with a measurement of $$x \sqrt{3}$$.
• The side opposite 90 degrees is the hypotenuse (longest side), with a length of $$2 x$$.
• For example, a 30-60-90 triangle may have side lengths of $$5,5 \sqrt{3}$$, and 10 .

Volume of a Rectangular Solid

$V=l w h$

$$l$$ is the length of one of the sides.
$$h$$ is the height of the figure.
$$w$$ is the width of one of the sides.

Volume of a Cylinder

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$V=\pi r^2 h$

$$r$$ is the radius of the circular side of the cylinder.
$$h$$ is the height of the cylinder.

Volume of a Sphere

$V=\left(\frac{4}{3}\right) \pi r^3$
$$r$$ is the radius of the sphere.

Volume of a Cone

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$V=\left(\frac{1}{3}\right) \pi r^2 h$

$$r$$ is the radius of the circular side of the cone.
$$h$$ is the height of the pointed part of the cone (as measured from the center of the circular part of the cone).

Volume of a Pyramid

$V=\left(\frac{1}{3}\right) l w h$
$$l$$ is the length of one of the edges of the rectangular part of the pyramid.
$$h$$ is the height of the figure at its peak (as measured from the center of the rectangular part of the pyramid).
$$w$$ is the width of one of the edges of the rectangular part of the pyramid.

Law: the number of degrees in a circle is 360
Law: the number of radians in a circle is $$2 \pi$$
Law: the number of degrees in a triangle is 180

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