Measurement and Circles Checkpoint
A free Geometry lesson from the “Measurement, Circles, and 3D Solids” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint mixes measurement skills: polygon area, composite area, surface area, volume, circle circumference and area, and fractional circle sectors. In Measurement, Circles, and 3D Solids, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Find area and volume
- Use circle formulas
- Work with arcs and sectors
Worked example
Problem. A 90-degree sector has circle area 80. Find the sector area.
- 90/360 = 1/4.
- The sector is one fourth of the circle.
- 80/4 = 20.
- Connect the result back to Measurement and Circles Checkpoint so the geometric relationship is explicit.
Answer: 20
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Find the area of a triangle with base 20 and height 7.
Show solution
- 1/2 x 20 x 7 = 70.
Answer: 70
2. Find the area of a trapezoid with bases 6 and 14 and height 8.
Show solution
- 1/2(20)(8) = 80.
Answer: 80
3. A 14 by 9 rectangle has a 3 by 6 section removed. What area remains?
Show solution
- 126 - 18 = 108.
Answer: 108
4. Find the volume of a rectangular prism that is 9 by 4 by 5.
Show solution
- 9 x 4 x 5 = 180.
Answer: 180
5. A cube has side length 7. What is its surface area?
Show solution
- Each face is 49.
- 6 x 49 = 294.
Answer: 294
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