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Geometry

Study Guide

Geometry makes up about 25% of the GED Math test. You need to calculate area, perimeter, volume, and surface area of common shapes, work with angles, and use the Pythagorean theorem.

1Area and Perimeter

Area measures the space inside a shape (square units). Perimeter measures the distance around a shape (linear units).

Examples:

•Rectangle: Area = l × w, Perimeter = 2l + 2w
•Triangle: Area = ½ × b × h
•Circle: Area = πr², Circumference = 2πr
•Trapezoid: Area = ½ × h × (b₁ + b₂)
2Volume and Surface Area

Volume measures the space inside a 3D shape (cubic units). Surface area measures the total area of all faces.

Examples:

•Rectangular prism: V = l × w × h
•Cylinder: V = πr²h
•Sphere: V = (4/3)πr³
•Cone: V = (1/3)πr²h
3Pythagorean Theorem

In a right triangle, a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle). Use this to find a missing side.

Examples:

•If a = 3 and b = 4: c² = 9 + 16 = 25, so c = 5
•If c = 13 and a = 5: b² = 169 - 25 = 144, so b = 12
4Angles

Complementary angles add to 90°. Supplementary angles add to 180°. Vertical angles (opposite angles when lines cross) are equal. The angles in a triangle always add to 180°.

Examples:

•If one angle in a triangle is 60° and another is 80°, the third is 180° - 60° - 80° = 40°
•If two angles are supplementary and one is 125°, the other is 55°
Key Formulas to Remember
1Area of rectangle: A = lw
2Area of triangle: A = ½bh
3Area of circle: A = πr²
4Circumference: C = 2πr
5Volume of rectangular prism: V = lwh
6Volume of cylinder: V = πr²h
7Pythagorean theorem: a² + b² = c²
8Surface area of cylinder: SA = 2πr² + 2πrh
Test-Taking Tips
The GED provides a formula sheet — practice using it so you know where each formula is.
Always check your units. Area is in square units, volume in cubic units.
Draw a diagram if one isn't provided. Label what you know and what you need to find.
Common Pythagorean triples to memorize: 3-4-5, 5-12-13, 8-15-17.