7th Grade Geometry: Concepts and Sample Problems

Seventh grade geometry can be tricky for some students because it can be hard to visualize many of the concepts, such as 3-D shapes and scale drawings. If you feel that your child needs additional practice, you can create your own geometry problems at home. Keep reading for a review of the concepts taught, as well as some sample problems and solutions.

Find available tutors

What Concepts Are Taught in 7th Grade Geometry?

In 7th grade, students learn to create scale drawings of shapes. For example, to double the size of a square with a length of 2 inches, each side would need to be 4 inches long. For more complicated problems, students may have to create proportional relationships to calculate the new lengths of the sides.

Students also work to conceptualize and make connections between 2-D and 3-D shapes. Students dissect 3-D objects and discover that they're made up of several 2-D objects. For instance, if a sphere was cut into slices, it would be made up of 2-D circles.

Also at this level, students learn to use formulas to calculate the circumference (c) and area (a) of a circle. Circumference is the length around a circle, while area is the space inside it. To calculate circumference and area, your child must be familiar with the mathematical constant Pi (p), which equals approximately 3.14, as well as the terms 'diameter' and 'radius.' Diameter (d) is the length of a straight line that passes through the center of a circle from one side to the other, and radius (r) is the length of a straight line that stretches from the center of a circle to its perimeter (in other words, half of the diameter). The formula for the circumference of a circle is c = p x d, while the formula for the area of a circle is a = p x r^2.

Finally, seventh graders figure out the measurement of unknown angles using what they know about supplementary angles (a pair of angles that add up to 180 degrees) and complementary angles (a pair of angels that add up to 90 degrees). For example, suppose one of two supplementary angles measures 160 degrees. What does the other measure? The other angle is 20 degrees because 180 - 160 = 20.

Sample Problems and Solutions

1. Create a 1/4 scale drawing of a rectangle that has a length of 36 centimeters (cm) and a width of 48 cm.

To calculate the new length and width, divide the two dimensions by four (36 ÷ 4 = 9 and 48 ÷ 4 = 12). The rescaled rectangle should be 9 cm long and 12 cm wide.

2. If you cut a cube into slices, what 2-dimensional shapes would result?

The 2-D shapes would be squares. If your child is having difficulty visualizing this problem, encourage him or her to draw a picture.

3. A circle's radius is 10 inches. What is the distance around the circle?

For this problem, your child will have to use the formula for circumference. He or she should begin by calculating the diameter, which can be determined by multiplying the radius by two (10 x 2 = 20). Then, your child should use the formula for circumference: c = p x d. He or she should substitute 3.14 for Pi, and plug in 20 for the diameter, so the equation should look like this: c = 3.14 x 20 = 62.8 inches.

4. Calculate the area of a circle with a 60 cm diameter.

First, have your child calculate the radius of the circle by dividing the diameter by two (60 ÷ 2 = 30). He or she can then utilize the formula for area (a= pi x r^2) to establish the equation a = 3.14 x 30^2. Your child should square the radius - 30^2 = 90 - and then multiply this number by Pi: 3.14 x 90 = 282.6. The area of the circle is 282.6 square centimeters.

5. An angle measures 30 degrees. What does the complementary angle measure?

Complementary angles create a right angle, which is 90 degrees. To solve this problem, your child should subtract 30 from 90 (90 - 30), so the complementary angle measures 60 degrees.
Did you find this useful? If so, please let others know!

Other Articles You May Be Interested In

  • More Blog Articles
    Not Your Father's Algebra As 45 States Look to Math Reform

    One plus one will always equal two...but just how students are taught math is going to change. Nearly every state in the country has adopted the Common Core Standards; for math, this means new and more in-depth approaches to teaching the subject. Have we seen the last of traditional algebra and geometry classes?

  • More Blog Articles
    The Pythagorean Theorem: Almost As Easy As ABC

    One of the most useful and widely used rules in mathematics is the Pythagorean theorem. Your child's mastery of this theorem is critical to success in geometry. One helpful method for understanding and remembering a rule like the Pythagorean theorem is to fully explore its meaning and history.

We Found 7 Tutors You Might Be Interested In

Huntington Learning

  • What Huntington Learning offers:
  • Online and in-center tutoring
  • One on one tutoring
  • Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online

K12

  • What K12 offers:
  • Online tutoring
  • Has a strong and effective partnership with public and private schools
  • AdvancED-accredited corporation meeting the highest standards of educational management
Online Only

Kaplan Kids

  • What Kaplan Kids offers:
  • Online tutoring
  • Customized learning plans
  • Real-Time Progress Reports track your child's progress
Online Only

Kumon

  • What Kumon offers:
  • In-center tutoring
  • Individualized programs for your child
  • Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online

Sylvan Learning

  • What Sylvan Learning offers:
  • Online and in-center tutoring
  • Sylvan tutors are certified teachers who provide personalized instruction
  • Regular assessment and progress reports
In-Home, In-Center and Online

Tutor Doctor

  • What Tutor Doctor offers:
  • In-Home tutoring
  • One on one attention by the tutor
  • Develops personlized programs by working with your child's existing homework
In-Home Only

TutorVista

  • What TutorVista offers:
  • Online tutoring
  • Student works one-on-one with a professional tutor
  • Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only

Help Your Child Succeed

Our Commitment to You

  • Free Help from Teachers

  • Free Learning Materials

  • Helping Disadvantaged Youth