What is Geometry Basics?

Master area, perimeter, and volume formulas for common shapes, understand angle relationships, and solve problems involving geometric properties.

How can I study Geometry Basics effectively?

Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 5 problems provided, checking solutions as you go. Regular review and active practice are key to retention.

Is this Geometry Basics study guide free?

Yes — all study notes, flashcards, and practice problems for Geometry Basics on Study Mondo are 100% free. No account is needed to access the content.

What course covers Geometry Basics?

Geometry Basics is part of the SAT Prep course on Study Mondo, specifically in the Additional Topics in Math section. You can explore the full course for more related topics and practice resources.

Are there practice problems for Geometry Basics?

Yes, this page includes 5 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.

Geometry Basics

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❓ Question:

A rectangle has a length of 12 and a width of 5. What is its perimeter and area?

Perimeter: $P = 2l + 2w = 2(12) + 2(5) = 24 + 10 = 34$

❓ Question:

Two parallel lines are cut by a transversal. One of the angles formed is 115°. What are the measures of all eight angles?

When parallel lines are cut by a transversal, we get two types of angles:

The angle of 115° and its vertical angle are both 115°. The supplementary angles are $180° - 115° = 65°$ .

All eight angles are either 115° or 65°:

Four angles of 115° (the angle, its vertical angle, and corresponding angles)
Four angles of 65° (supplementary to the 115° angles)

Answer: Four angles are 115° and four are 65°.

Key relationships used: vertical angles, corresponding angles, supplementary angles.

❓ Question:

A rectangular box has dimensions 3 × 4 × 12. What is the length of the longest diagonal inside the box?

3D diagonal formula: $d = \sqrt{l^2 + w^2 + h^2}$

$d = \sqrt{3^2 + 4^2 + 12^2} = \sqrt{9 + 16 + 144} = \sqrt{169} = 13$

Answer: The space diagonal is 13.

Alternatively: First find the diagonal of the base: $\sqrt{3^2 + 4^2} = 5$ (3-4-5 triple), then use that with the height: (5-12-13 triple).

❓ Question:

The volume of a cylinder is $100\pi$ cubic cm and its height is 4 cm. What is the total surface area?

Step 1: Find the radius using the volume formula: $V = \pi r^2 h$ $100\pi = \pi r^2 (4)$ $r^2 = 25$ $r = 5 \text{ cm}$

Step 2: Calculate total surface area (two circles + lateral surface): $SA = 2\pi r^2 + 2\pi rh$ $= 2\pi(25) + 2\pi(5)(4)$

Answer: $90\pi$ cm² (approximately 282.74 cm²)

❓ Question:

Two similar triangles have corresponding sides in the ratio $3:5$ . If the area of the smaller triangle is 27 cm², what is the area of the larger triangle?

Key property of similar figures: If corresponding sides have ratio $k$ , then areas have ratio $k^2$ .

Side ratio: $\frac{3}{5}$

Area ratio: $\left(\frac{3}{5}\right)^2 = \frac{9}{25}$

$\frac{27}{A_{\text{large}}} = \frac{9}{25}$

Answer: 75 cm²

Remember: Side ratio = $k$ , Area ratio = $k^2$ , Volume ratio = $k^3$ .

Geometry Basics

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