Geometry Formulas for ASVAB and PiCAT

Introduction

• Essential geometry formulas needed for the ASVAB and PiCAT tests.
• No reference sheet allowed during these tests.
• Knowing these 10 formulas is crucial for success.
• Encouragement to learn even if only 4-5 are known.

Key Geometry Formulas

1. Area of a Triangle

• Formula: ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} )
• Note: Height can be inside, outside, or far outside the triangle.

2. Pythagorean Theorem

• Formula: ( a^2 + b^2 = c^2 )
  • (a) and (b) are the legs of a right triangle.
  • (c) is the hypotenuse, directly across from the right angle.
• Use to solve for any missing side if two are known.

3. Area and Circumference of a Circle

• Area: ( \pi r^2 )
  • (r) is the radius.
  • (\pi) is approximated by 3.14 or (\frac{22}{7}).
• Circumference:
  • ( C = \pi d ) or ( C = 2\pi r )

4. Perimeter and Area of a Square

• Perimeter: ( 4s ) (where (s) is the side length)
• Area: ( s^2 )

5. Perimeter and Area of a Rectangle

• Perimeter: ( 2l + 2w )
• Area: ( l \times w )

6. Area of a Parallelogram

• Formula: ( \text{Area} = \text{base} \times \text{height} )

7. Volume of a Rectangular Prism

• Formula: ( l \times w \times h )

Additional Formulas

8. Volume of a Cylinder

• Volume: ( \pi r^2 \times h )
  • Use the area of the circular face (\pi r^2) multiplied by the height.

9. Slope of a Line

• Formula: ( m = \frac{y_2 - y_1}{x_2 - x_1} )
  • Derived from two points ((x_1, y_1)) and ((x_2, y_2)).

Study and Practice

• Memorizing formulas is key, but understanding and applying them is essential.
• Practice through additional resources like the provided geometry review playlist.
• Playlist contains practice test questions covering these formulas.

Conclusion

• Mastery of these formulas is crucial for success on the ASVAB and PiCAT.
• Recommended to check out additional resources for practice.
• Support the channel by subscribing and sharing content on social media.

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• Related Resources: Geometry review playlist link provided in video description.
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