NeSA-M High School Reference Sheet
Shape
Area
Key
Circumference
Circle
A = r2
C = πd = 2πr
Triangle
1
A = 2 bh
Rectangle
A = lw
Trapezoid
A = 12 h (b1 + b2)
Parallelogram
A = bh
b = base
w = width
Perimeter
B = area of base
d = diameter
P = 2l + 2w
h = height
r = radius
l = length
ℓ = slant
Use 3.14 for π
Volume
3-Dimensional Shape
Total Surface Area
Right Circular Cone
V = 13 r2h
T =
Pyramid
V = 13 Bh
T =
Sphere
V = 43 r3
T = 4r2
Right Circular Cylinder
V = r2h
T = 2rh + 2r2
Right Prism
V = Bh
T = 2B + Ph
1
2 (2r)ℓ +
B + 12 Pℓ
r2 + rℓ + r2
Formulas
Pythagorean Theorem
Distance, rate, and time formula, where
d = distance, r = rate, t = time:
c
a
d = rt
b
c2 = a2 + b2
Right-Triangle Relationships
30º-60º-90º Triangle
Relationships
Trigonometric Ratios
B
c
a
C
b
sin A = ac
cos A = bc
tan A = a
b
A
45º-45º-90º Triangle
Relationships
B
B
x
C
60°
45°
2x
30°
x√3
x√2
A
A
x
45°
x
C
NeSA-M High School Reference Sheet
Coordinate Geometry
Linear Equation Forms
Given: Points A(x1, y1), B(x2, y2)
Distance between two points:
Point-Slope Form:
y – y1 = m (x – x1)
AB =
(x2 – x1)2 + (y2– y1)2
Standard of General Form:
Midpoint between two points:
Ax + By = C
x2 + x1 y2 + y1
,
2
2
y –y
Slope of line through two points: m = x2 – x1
2
1
Midpoint of AB =
Slope-Intercept Form:
y = mx + b
(
Equation of a Circle
Quadratic Formula
(x – h)2 + (y – k)2 = r2
2
x = –b ± √ b – 4ac
2a
2
ax + bx + c = 0
(h, k) = center
r = radius
Standard Units
)
Metric Units
Conversions – Length
1 foot (ft) = 12 inches (in.)
1 centimeter (cm) = 10 millimeters (mm)
1 yard (yd) = 3 feet (ft) = 36 inches (in.)
1 meter (m) = 100 centimeters (cm)
1 mile (mi) = 1,760 yards (yd) = 5,280 feet (ft)
1 kilometer (km) = 1,000 meters (m)
Conversions – Area
1 square foot (sq. ft) = 144 square inches (sq. in.)
1 square yard (sq. yd) = 9 square feet (sq. ft)
Conversions – Volume
1 cubic yard (cu. yd) = 27 cubic feet (cu. ft)
1 cubic foot (cu. ft) = 1,728 cubic in. (cu. in.)
Conversions – Capacity
1 cup = 8 fluid ounces (fl oz)
1 liter (l) = 1,000 milliliters (ml)
1 pint (pt) = 2 cups
1 liter (l) = 1,000 cubic centimeters (cu. cm)
1 quart (qt) = 2 pints (pt)
1 kiloliter (kl) = 1,000 liters (l)
1 gallon (gal.) = 4 quarts (qt)
Conversions – Weight/Mass
1 pound (lb) = 16 ounces (oz)
1 gram (g) = 1,000 milligrams (mg)
1 ton = 2,000 pounds (lb)
1 kilogram (kg) = 1,000 grams (g)