Elementary Geometry Problems, Solutions and Explanations

In elementary school, students learn to recognize basic shapes, like squares, circles and triangles. They also learn the formulas for area (the amount of surface that a 2-dimensional shape covers) and perimeter (the distance around the outside of a 2-dimensional shape). In later grades, teachers may show students how to measure angles and work with lines, segments and rays. If your child needs additional geometry practice, try using the following guidelines to create practice problems at home.

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What Do Elementary Geometry Problems Include?

Most elementary geometry problems include a picture, which can help students visualize the shape. Especially when students work with 3-dimensional objects, it can be difficult for them to comprehend that an object has multiple sides - for example, a cube has six sides - unless they can see it.

You might, however, challenge your child by describing a shape rather than presenting him or her with a visual image. For example, you might ask your child to identify and draw a shape that has two long sides and two short sides. This can help him or her review the characteristics of basic shapes.

When students are learning about angles, teachers often provide drawings on a worksheet and ask students to measure them using a protractor. Not only will this give your child practice using the tool, but it can also be a lesson in precision. You also might teach your child the terms 'acute' (an angle less than 90 degrees), 'obtuse' (an angle from 90-180 degrees) and 'right' (an angle of exactly 90 degrees) and ask him or her to label various angles.

Geometry Problems and Solutions by Grade Level


1.Which of the following are attributes of a shape: color, sides, points or size?

In first grade, students learn to identify shapes based on their characteristics, like the number of sides or points. They also learn which out characteristics can't help to identify shapes, such as color and size.

2. Which of the following are 3-dimensional: square, triangle, cone, circle or cube?

First graders learn to create both 2-dimensional and 3-dimensional shapes. If your child has trouble remembering the names, you can provide pictures to make the difference more clear. He or she should identify cones and cubes as 3-dimensional shapes.


1. Draw three quadrilaterals.

In second grade, students learn more advanced categories for shapes. These can include quadrilaterals (4-sided figures), pentagons (5-sided figures) and hexagons (6-sided figures). This kind of question fosters creativity because it is open-ended. Just be sure your child's drawings have four sides.

2. Draw a rectangle, and divide it into thirds. Do all the partitions look the same?

Partitioning shapes is a large part of elementary geometry. This type of activity can help prepare your child for future work with fractions because he or she will be thinking about parts of a whole. While the partitioning in this particular question likely will result in three equally sized, smaller rectangles, it's important that your child realizes that equal shares of identical wholes won't always have the same shape.


1. Calculate the perimeter of a fence that is 10 feet by 12 feet.

To find the perimeter (p), add the lengths of all the sides. In this case, the calculation should look like this: p = 10 + 10 + 12 + 12 = 44 feet.

2. What is the area of a rectangle that is 5 inches long and 2 inches wide?

Since third graders have learned multiplication, they should be able to calculate the area of a shape. The formula for area (a) is a = length (l) x width (w). In this case, the area of the rectangle is 10 square inches.
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