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 3D 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.
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 2D and 3D shapes. Students dissect 3D objects and discover that they're made up of several 2D objects. For instance, if a sphere was cut into slices, it would be made up of 2D 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 2dimensional shapes would result?
 The 2D 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.
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