Geometry Blueprint Reference
Geometry Blueprint
Student Reference • Grades 3-5
SHEET NO: 1 OF 2
REF: NC.3-5.G/MD
Grades 3 - 4: Foundations
Perimeter (P)
The total distance around the outside.
\[ P = s_1 + s_2 + s_3 + s_4 \]
Measured in Linear Units (in, cm, ft)
Area (A)
The amount of space inside a 2D shape.
\[ A = l \times w \]
Measured in Square Units (\(u^2\))
Square
4 Equal Sides
4 Right Angles
Rectangle
Opposite Sides Equal
4 Right Angles
Triangle
3 Sides
3 Angles
Rhombus
4 Equal Sides
Opposite Angles Equal
Grade 5: Volume
Volume (V)
Measuring space inside a 3D object.
Rectangular Prism Formula
\[ V = l \times w \times h \]
ALTERNATIVE VERSION
\[ V = B \times h \]
\(B = \text{Area of the Base } (l \times w)\)
Measured in Cubic Units (\(u^3\)).
Think: How many unit cubes fit inside?
Conversion Standards
Length Reference
1 foot (ft) 12 inches (in)
1 yard (yd) 3 feet (ft)
1 mile (mi) 5,280 feet (ft)
1 meter (m) 100 centimeters (cm)
1 kilometer (km) 1,000 meters (m)
Liquid Volume Benchmarks
1 Gal = 4 Qt
1 Qt = 2 Pt
1 Pt = 2 Cups
1 Cup = 8 fl oz
Geometry Blueprint
Advanced Analysis • Grades 6-8
SHEET NO: 2 OF 2
REF: NC.6-8.G/MD
Grade 6: Area & Surface Area
Polygon Area
Triangle \[ A = \frac{1}{2}bh \]
Parallelogram \[ A = bh \]
Trapezoid \[ A = \frac{1}{2}(b_1 + b_2)h \]
Surface Area (SA)
Sum of areas of all faces.
Rectangular Prism
\[ SA = 2lw + 2lh + 2wh \]
Pro Tip:
Visualize the Net!
Grade 7: Angles & Circles
Angle Relationships
Complementary Sum = 90°
Supplementary Sum = 180°
Vertical Equal Pairs
Circle Geometry
C r
Circumference (C)
\[ C = 2\pi r \text{ or } \pi d \]
Area (A)
\[ A = \pi r^2 \]
Grade 8: Pro Analysis
Pythagorean Theorem
\[ a^2 + b^2 = c^2 \]
a b c
c = Hypotenuse
Longest side opposite the right angle.
Curved Surface Volume
Cylinder \[ V = \pi r^2 h \]
Cone \[ V = \frac{1}{3} \pi r^2 h \]
Sphere \[ V = \frac{4}{3} \pi r^3 \]
L/W/H: Length, Width, Height
b/h: Base, Height (2D)
r/d: Radius, Diameter
B: Area of 3D Base
Master Geometry Reference
Property of Student • Grade Band 3-8 NC.G
