8th Grade Geometry Worksheets with Answers (PDF)

In eighth grade, students use the Pythagorean relationship (a² + b² = c²) to find missing side lengths in right triangles and to test whether a given triangle contains a right angle. They square the known measurements, add or subtract those values, and take square roots to determine the unknown length.

A frequent error happens when solving for a missing leg. Students often add the squares of the two given side lengths automatically, forgetting that finding a leg requires subtracting the known leg's square from the hypotenuse's square. Another common slip is carrying out the arithmetic correctly but forgetting to take the square root at the end, leaving the answer as c² instead of c.

Practice tasks provide triangle diagrams or lists of three side measurements. Exercises typically take three forms: Find the hypotenuse when both legs are provided, Find a leg of a right triangle when the hypotenuse and one leg are known, and Is the triangle right-angled? where students substitute three side lengths into the formula to check if the equation holds true.

In eighth grade, students learn to know and apply the volume formulas for three curved three-dimensional shapes: cylinders, cones, and spheres. They identify given measurements such as radius, diameter, or height, apply exponents by squaring or cubing values, and use multiplication with pi to find total volume.

A common mistake is mixing up radius and diameter, leading students to square or cube the full width across the shape instead of half of it. Another frequent error is confusing the powers and fractional coefficients across shapes—such as squaring the radius instead of cubing it for a sphere, or forgetting to multiply by 1/3 for a cone or 4/3 for a sphere.

Tasks on printable worksheets are organized around three focused formats: Volume of a cylinder, Volume of a cone, and Volume of a sphere. Students work from geometric diagrams or word problems displaying measurements to compute the correct volume for each solid.

Students use the foundational geometric facts that the interior angles of a triangle add up to 180 degrees and the interior angles of a quadrilateral add up to 360 degrees. To find an unknown angle, they add the given angle measures and subtract that combined total from either 180 or 360 degrees.

A frequent error is mixing up the two target totals, such as attempting to subtract three angles of a four-sided shape from 180 degrees instead of 360 degrees. Arithmetic slips also occur during the multi-step addition when summing the known values before the final subtraction.

In practice, tasks come from two core templates: The third angle of a triangle, where two angle measures are provided and students solve for the remaining one, and The fourth angle of a quadrilateral, where students are given three angle values and calculate the final missing angle.